TSTP Solution File: SWW621_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW621_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 20:59:28 EDT 2022
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW621_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 : n017.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 19:48:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.21/0.52 % SZS status Theorem
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 tff(occ1_type, type, (
% 0.21/0.52 occ1: ( ty * uni * uni * $int * $int ) > $int)).
% 0.21/0.52 tff(tptp_fun_I1_23_type, type, (
% 0.21/0.52 tptp_fun_I1_23: $int)).
% 0.21/0.52 tff(tptp_fun_L_13_type, type, (
% 0.21/0.52 tptp_fun_L_13: $int)).
% 0.21/0.52 tff(t2tb3_type, type, (
% 0.21/0.52 t2tb3: map_int_elt > uni)).
% 0.21/0.52 tff(tptp_fun_Tmp1_16_type, type, (
% 0.21/0.52 tptp_fun_Tmp1_16: map_int_elt)).
% 0.21/0.52 tff(t2tb2_type, type, (
% 0.21/0.52 t2tb2: elt1 > uni)).
% 0.21/0.52 tff(tptp_fun_V_24_type, type, (
% 0.21/0.52 tptp_fun_V_24: elt1)).
% 0.21/0.52 tff(elt_type, type, (
% 0.21/0.52 elt: ty)).
% 0.21/0.52 tff(tb2t_type, type, (
% 0.21/0.52 tb2t: uni > $int)).
% 0.21/0.52 tff(t2tb_type, type, (
% 0.21/0.52 t2tb: $int > uni)).
% 0.21/0.52 tff(tptp_fun_K_18_type, type, (
% 0.21/0.52 tptp_fun_K_18: $int)).
% 0.21/0.52 tff(set_type, type, (
% 0.21/0.52 set: ( ty * ty * uni * uni * uni ) > uni)).
% 0.21/0.52 tff(get_type, type, (
% 0.21/0.52 get: ( ty * ty * uni * uni ) > uni)).
% 0.21/0.52 tff(tptp_fun_I_20_type, type, (
% 0.21/0.52 tptp_fun_I_20: $int)).
% 0.21/0.52 tff(int_type, type, (
% 0.21/0.52 int: ty)).
% 0.21/0.52 tff(tptp_fun_A2_19_type, type, (
% 0.21/0.52 tptp_fun_A2_19: map_int_elt)).
% 0.21/0.52 tff(tptp_fun_I_6_type, type, (
% 0.21/0.52 tptp_fun_I_6: ( $int * $int * uni * uni * ty ) > $int)).
% 0.21/0.52 tff(sort1_type, type, (
% 0.21/0.52 sort1: ( ty * uni ) > $o)).
% 0.21/0.52 tff(tptp_fun_A3_22_type, type, (
% 0.21/0.52 tptp_fun_A3_22: map_int_elt)).
% 0.21/0.52 tff(tb2t3_type, type, (
% 0.21/0.52 tb2t3: uni > map_int_elt)).
% 0.21/0.52 tff(tptp_fun_J_21_type, type, (
% 0.21/0.52 tptp_fun_J_21: $int)).
% 0.21/0.52 tff(tptp_fun_R_11_type, type, (
% 0.21/0.52 tptp_fun_R_11: $int)).
% 0.21/0.52 tff(tb2t2_type, type, (
% 0.21/0.52 tb2t2: uni > elt1)).
% 0.21/0.52 tff(tptp_fun_A1_14_type, type, (
% 0.21/0.52 tptp_fun_A1_14: map_int_elt)).
% 0.21/0.52 tff(tptp_fun_A_15_type, type, (
% 0.21/0.52 tptp_fun_A_15: $int)).
% 0.21/0.52 tff(tptp_fun_M_12_type, type, (
% 0.21/0.52 tptp_fun_M_12: $int)).
% 0.21/0.52 tff(le1_type, type, (
% 0.21/0.52 le1: ( elt1 * elt1 ) > $o)).
% 0.21/0.52 tff(sorted_sub1_type, type, (
% 0.21/0.52 sorted_sub1: ( array_elt * $int * $int ) > $o)).
% 0.21/0.52 tff(tb2t1_type, type, (
% 0.21/0.52 tb2t1: uni > array_elt)).
% 0.21/0.52 tff(mk_array1_type, type, (
% 0.21/0.52 mk_array1: ( ty * $int * uni ) > uni)).
% 0.21/0.52 tff(tptp_fun_Tmp_17_type, type, (
% 0.21/0.52 tptp_fun_Tmp_17: $int)).
% 0.21/0.52 tff(map_type, type, (
% 0.21/0.52 map: ( ty * ty ) > ty)).
% 0.21/0.52 tff(1,assumption,(~($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0)), introduced(assumption)).
% 0.21/0.52 tff(2,assumption,(~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))), introduced(assumption)).
% 0.21/0.52 tff(3,plain,
% 0.21/0.52 (($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0))) | (~$lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(4,plain,
% 0.21/0.52 (~$lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.21/0.52 tff(5,plain,
% 0.21/0.52 (^[X: $int] : refl(sort1(int, t2tb(X)) <=> sort1(int, t2tb(X)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(6,plain,
% 0.21/0.52 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.52 tff(7,plain,
% 0.21/0.52 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(8,axiom,(![X: $int] : sort1(int, t2tb(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort')).
% 0.21/0.52 tff(9,plain,
% 0.21/0.52 (![X: $int] : sort1(int, t2tb(X))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.52 tff(10,plain,(
% 0.21/0.52 ![X: $int] : sort1(int, t2tb(X))),
% 0.21/0.52 inference(skolemize,[status(sab)],[9])).
% 0.21/0.52 tff(11,plain,
% 0.21/0.52 (![X: $int] : sort1(int, t2tb(X))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.52 tff(12,plain,
% 0.21/0.52 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(13,plain,
% 0.21/0.52 (sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.52 tff(14,plain,
% 0.21/0.52 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(K!18))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(15,plain,
% 0.21/0.52 (sort1(int, t2tb(K!18))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.52 tff(16,plain,
% 0.21/0.52 (^[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)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(17,plain,
% 0.21/0.52 (![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))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.52 tff(18,plain,
% 0.21/0.52 (^[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))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(19,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.52 tff(20,plain,
% 0.21/0.52 (^[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))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(21,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.52 tff(22,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[21, 19])).
% 0.21/0.52 tff(23,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(24,plain,
% 0.21/0.52 (^[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)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(25,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.52 tff(26,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/sandbox/benchmark/theBenchmark.p','select_neq')).
% 0.21/0.52 tff(27,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.52 tff(28,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.52 tff(29,plain,(
% 0.21/0.52 ![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)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[28])).
% 0.21/0.52 tff(30,plain,
% 0.21/0.52 (![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)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.52 tff(31,plain,
% 0.21/0.52 (![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))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.21/0.52 tff(32,plain,
% 0.21/0.52 (((~![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, t2tb(K!18))) | (~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))) <=> ((~![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, t2tb(K!18))) | (~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(33,plain,
% 0.21/0.52 (((~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~sort1(int, t2tb(K!18))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))) <=> ((~sort1(int, t2tb(K!18))) | (~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(34,plain,
% 0.21/0.52 (((~![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, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~sort1(int, t2tb(K!18))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))) <=> ((~![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, t2tb(K!18))) | (~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.53 tff(35,plain,
% 0.21/0.53 (((~![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, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~sort1(int, t2tb(K!18))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))) <=> ((~![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, t2tb(K!18))) | (~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.53 tff(36,plain,
% 0.21/0.53 ((~![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, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~sort1(int, t2tb(K!18))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(37,plain,
% 0.21/0.53 ((~![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, t2tb(K!18))) | (~sort1(int, t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | ![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.53 tff(38,plain,
% 0.21/0.53 (![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[37, 31, 15, 13])).
% 0.21/0.53 tff(39,plain,
% 0.21/0.53 (($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0))) | (~(get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(40,plain,
% 0.21/0.53 (~(get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[39, 2])).
% 0.21/0.53 tff(41,plain,
% 0.21/0.53 (((~![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))) | ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))) <=> ((~![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))) | (t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(42,plain,
% 0.21/0.53 ((~![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))) | ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(43,plain,
% 0.21/0.53 ((~![B1: uni] : ((t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), B1), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))))) | (t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.53 tff(44,plain,
% 0.21/0.53 (t2tb(K!18) = t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[43, 40, 38])).
% 0.21/0.53 tff(45,plain,
% 0.21/0.53 (t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)) = t2tb(K!18)),
% 0.21/0.53 inference(symmetry,[status(thm)],[44])).
% 0.21/0.53 tff(46,plain,
% 0.21/0.53 (tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = tb2t(t2tb(K!18))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.53 tff(47,plain,
% 0.21/0.53 (tb2t(t2tb(K!18)) = tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))),
% 0.21/0.53 inference(symmetry,[status(thm)],[46])).
% 0.21/0.53 tff(48,plain,
% 0.21/0.53 ((~(tb2t(t2tb(K!18)) = tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))) | $lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))), 0)),
% 0.21/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.53 tff(49,plain,
% 0.21/0.53 ($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))), 0)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.53 tff(50,plain,
% 0.21/0.53 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(51,plain,
% 0.21/0.53 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.53 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.53 tff(52,plain,
% 0.21/0.53 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t(t2tb(I)), $product(-1, I)) = $sum($product(-1, I), tb2t(t2tb(I)))), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t(t2tb(I))) = 0))), rewrite(($sum($product(-1, I), tb2t(t2tb(I))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(53,plain,
% 0.21/0.53 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.53 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.53 tff(54,plain,
% 0.21/0.53 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(55,plain,
% 0.21/0.53 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.21/0.53 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.53 tff(56,plain,
% 0.21/0.53 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(57,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 0.21/0.53 tff(58,plain,
% 0.21/0.53 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.54 tff(59,plain,
% 0.21/0.54 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.21/0.54 tff(60,plain,
% 0.21/0.54 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[59, 53])).
% 0.21/0.54 tff(61,plain,(
% 0.21/0.54 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.54 inference(skolemize,[status(sab)],[60])).
% 0.21/0.54 tff(62,plain,
% 0.21/0.54 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.21/0.54 tff(63,plain,
% 0.21/0.54 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))) = 0)),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(64,plain,
% 0.21/0.54 ($sum(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))) = 0),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.54 tff(65,plain,
% 0.21/0.54 ((~($sum(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))) = 0)) | $greatereq($sum(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))), 0)),
% 0.21/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.54 tff(66,plain,
% 0.21/0.54 ($greatereq($sum(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt), $product(-1, tb2t(t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))))), 0)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.54 tff(67,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(theory_lemma,[status(thm)],[66, 49, 4])).
% 0.21/0.54 tff(68,plain,($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(69,plain,
% 0.21/0.54 (^[A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : refl(((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)) <=> ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(70,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)) <=> ![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.54 tff(71,plain,
% 0.21/0.54 (^[A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : rewrite(((~((~($lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)) <=> ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(72,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~((~($lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)) <=> ![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.54 tff(73,plain,
% 0.21/0.54 (^[A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : rewrite(((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> ((~![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(74,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> ![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.54 tff(75,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> ![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(76,plain,
% 0.21/0.54 (^[A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : trans(monotonicity(quant_intro(proof_bind(^[I: $int] : trans(monotonicity(rewrite(($lesseq(L, I) & $less(I, U)) <=> ($lesseq(L, I) & (~$lesseq(U, I)))), ((($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) <=> (($lesseq(L, I) & (~$lesseq(U, I))) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))))), rewrite((($lesseq(L, I) & (~$lesseq(U, I))) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) <=> ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))), ((($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) <=> ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))))), (![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) <=> ![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))))), ((![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) => (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> (![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) => (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))))), rewrite((![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) => (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))), ((![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) => (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(77,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : (![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) => (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U))) <=> ![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.54 tff(78,axiom,(![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : (![I: $int] : (($lesseq(L, I) & $less(I, U)) => (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I)))) => (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','occ_eq')).
% 0.21/0.54 tff(79,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.54 tff(80,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq(L, I) & (~$lesseq(U, I)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | (occ1(A, V, M1, L, U) = occ1(A, V, M2, L, U)))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.54 tff(81,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~![I: $int] : ((~($lesseq($sum(L, $product(-1, I)), 0) & (~$lesseq($sum(U, $product(-1, I)), 0)))) | (get(A, int, M1, t2tb(I)) = get(A, int, M2, t2tb(I))))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[80, 74])).
% 0.21/0.54 tff(82,plain,(
% 0.21/0.54 ![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~((~($lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) & (~$lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(skolemize,[status(sab)],[81])).
% 0.21/0.54 tff(83,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.21/0.54 tff(84,plain,
% 0.21/0.54 (![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[83, 70])).
% 0.21/0.54 tff(85,plain,
% 0.21/0.54 (((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | ((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0))) <=> ((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | (~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(86,plain,
% 0.21/0.54 (((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))) = 0)) <=> ((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(87,plain,
% 0.46/0.54 (((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | ((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))) = 0))) <=> ((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | ((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0)))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[86])).
% 0.46/0.55 tff(88,plain,
% 0.46/0.55 (((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | ((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))) = 0))) <=> ((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | (~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0))),
% 0.46/0.55 inference(transitivity,[status(thm)],[87, 85])).
% 0.46/0.55 tff(89,plain,
% 0.46/0.55 ((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | ((~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))) = 0))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(90,plain,
% 0.46/0.55 ((~![A: ty, V: uni, M1: uni, M2: uni, L: $int, U: $int] : ((~($lesseq($sum(U, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0) | (get(A, int, M1, t2tb(tptp_fun_I_6(U, L, M2, M1, A))) = get(A, int, M2, t2tb(tptp_fun_I_6(U, L, M2, M1, A)))) | (~$lesseq($sum(L, $product(-1, tptp_fun_I_6(U, L, M2, M1, A))), 0)))) | ($sum(occ1(A, V, M1, L, U), $product(-1, occ1(A, V, M2, L, U))) = 0))) | (~($lesseq($sum(tb2t(t2tb(K!18)), $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))) = get(elt, int, t2tb3(A2!19), t2tb(tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt)))) | (~$lesseq($sum(L!13, $product(-1, tptp_fun_I_6(tb2t(t2tb(K!18)), L!13, t2tb3(A2!19), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), elt))), 0)))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.46/0.55 tff(91,plain,
% 0.46/0.55 ($false),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[90, 84, 68, 1])).
% 0.46/0.55 tff(92,plain,($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0), inference(lemma,lemma(discharge,[]))).
% 0.46/0.55 tff(93,plain,
% 0.46/0.55 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(94,plain,
% 0.46/0.55 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.46/0.55 tff(95,plain,
% 0.46/0.55 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(K!18, $product(-1, tb2t(t2tb(K!18)))) = 0)),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(96,plain,
% 0.46/0.55 ($sum(K!18, $product(-1, tb2t(t2tb(K!18)))) = 0),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[95, 62])).
% 0.46/0.55 tff(97,plain,
% 0.46/0.55 ((~($sum(K!18, $product(-1, tb2t(t2tb(K!18)))) = 0)) | $lesseq($sum(K!18, $product(-1, tb2t(t2tb(K!18)))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(98,plain,
% 0.46/0.55 ($lesseq($sum(K!18, $product(-1, tb2t(t2tb(K!18)))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.46/0.55 tff(99,plain,
% 0.46/0.55 ((~($sum(K!18, $product(-1, tb2t(t2tb(K!18)))) = 0)) | $greatereq($sum(K!18, $product(-1, tb2t(t2tb(K!18)))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(100,plain,
% 0.46/0.55 ($greatereq($sum(K!18, $product(-1, tb2t(t2tb(K!18)))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.46/0.55 tff(101,plain,
% 0.46/0.55 (K!18 = tb2t(t2tb(K!18))),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[100, 98])).
% 0.46/0.55 tff(102,plain,
% 0.46/0.55 (tb2t(t2tb(K!18)) = K!18),
% 0.46/0.55 inference(symmetry,[status(thm)],[101])).
% 0.46/0.55 tff(103,plain,
% 0.46/0.55 (occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))) = occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)),
% 0.46/0.55 inference(monotonicity,[status(thm)],[102])).
% 0.46/0.55 tff(104,plain,
% 0.46/0.55 (occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18) = occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18)))),
% 0.46/0.55 inference(symmetry,[status(thm)],[103])).
% 0.46/0.55 tff(105,plain,
% 0.46/0.55 ((~(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18) = occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(106,plain,
% 0.46/0.55 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.46/0.55 tff(107,plain,
% 0.46/0.55 (($greatereq($sum(R!11, $product(-1, L!13)), 1) & ($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)) & ((~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & $greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0)))) <=> ($greatereq($sum(R!11, $product(-1, L!13)), 1) & $greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11) & (~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0)))),
% 0.46/0.55 inference(rewrite,[status(thm)],[])).
% 0.46/0.55 tff(108,plain,
% 0.46/0.55 (((~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & ($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0))) & ($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0))) & ($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0))) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & ($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0))) & ($lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) & ($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1)) & (~($sum(R!11, $product(-1, J!21)) = 0))) <=> ((~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & $greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0)))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(109,plain,
% 0.46/0.56 ((~($sum(J!21, $product(-1, R!11)) = 0)) <=> (~($sum(R!11, $product(-1, J!21)) = 0))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(110,plain,
% 0.46/0.56 ((~(~($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1)))) <=> ($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(111,plain,
% 0.49/0.56 ((~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1))) <=> (~($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(112,plain,
% 0.49/0.56 ((~(~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1)))) <=> (~(~($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1))))),
% 0.49/0.56 inference(monotonicity,[status(thm)],[111])).
% 0.49/0.56 tff(113,plain,
% 0.49/0.56 ((~(~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1)))) <=> ($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1))),
% 0.49/0.56 inference(transitivity,[status(thm)],[112, 110])).
% 0.49/0.56 tff(114,plain,
% 0.49/0.56 (($greatereq($sum(I!20, $product(-1, L!13)), 0) & $lesseq($sum(I!20, $product(-1, M!12)), 0) & $greatereq($sum(J!21, $product(-1, M!12)), 0) & $lesseq($sum(J!21, $product(-1, R!11)), 0) & ($sum(I!20, $sum($product(-1, K!18), $sum(J!21, $product(-1, M!12)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)), occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) <=> ($lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(115,plain,
% 0.49/0.56 ((~(~($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0))))) <=> ($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(116,plain,
% 0.49/0.56 ((~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0)))) <=> (~($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(117,plain,
% 0.49/0.56 ((~(~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0))))) <=> (~(~($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)))))),
% 0.49/0.56 inference(monotonicity,[status(thm)],[116])).
% 0.49/0.56 tff(118,plain,
% 0.49/0.56 ((~(~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0))))) <=> ($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)))),
% 0.49/0.56 inference(transitivity,[status(thm)],[117, 115])).
% 0.49/0.56 tff(119,plain,
% 0.49/0.56 ((~(~le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))))) <=> le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(120,plain,
% 0.49/0.56 ((~(~($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0))))) <=> ($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(121,plain,
% 0.49/0.56 ((~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0)))) <=> (~($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(122,plain,
% 0.49/0.56 ((~(~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0))))) <=> (~(~($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)))))),
% 0.49/0.56 inference(monotonicity,[status(thm)],[121])).
% 0.49/0.56 tff(123,plain,
% 0.49/0.56 ((~(~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0))))) <=> ($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)))),
% 0.49/0.56 inference(transitivity,[status(thm)],[122, 120])).
% 0.49/0.56 tff(124,plain,
% 0.49/0.56 ((~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0))))) <=> ($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(125,plain,
% 0.49/0.56 ((~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0)))) <=> (~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(126,plain,
% 0.49/0.56 ((~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0))))) <=> (~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)))))),
% 0.49/0.56 inference(monotonicity,[status(thm)],[125])).
% 0.49/0.56 tff(127,plain,
% 0.49/0.56 ((~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0))))) <=> ($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)))),
% 0.49/0.56 inference(transitivity,[status(thm)],[126, 124])).
% 0.49/0.56 tff(128,plain,
% 0.49/0.56 ((($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))) & (($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) <=> ($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(129,plain,
% 0.49/0.56 (((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0))) <=> (($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(130,plain,
% 0.49/0.56 ((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) <=> ($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(131,plain,
% 0.49/0.56 (((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) & ((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) <=> (($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))) & (($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0))))),
% 0.49/0.56 inference(monotonicity,[status(thm)],[130, 129])).
% 0.49/0.56 tff(132,plain,
% 0.49/0.56 (((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) & ((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) <=> ($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))),
% 0.49/0.56 inference(transitivity,[status(thm)],[131, 128])).
% 0.49/0.56 tff(133,plain,
% 0.49/0.56 ((~$greatereq($sum(I!20, $product(-1, M!12)), 0)) <=> (~$lesseq($sum(M!12, $product(-1, I!20)), 0))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(134,plain,
% 0.49/0.56 (((~$greatereq($sum(I!20, $product(-1, M!12)), 0)) & ((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) & ((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) & (~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0))))) & (~(~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0))))) & (~(~le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))))) & (~(~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0))))) & ($greatereq($sum(I!20, $product(-1, L!13)), 0) & $lesseq($sum(I!20, $product(-1, M!12)), 0) & $greatereq($sum(J!21, $product(-1, M!12)), 0) & $lesseq($sum(J!21, $product(-1, R!11)), 0) & ($sum(I!20, $sum($product(-1, K!18), $sum(J!21, $product(-1, M!12)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)), occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) & (~(~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1)))) & (~($sum(J!21, $product(-1, R!11)) = 0))) <=> ((~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & ($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0))) & ($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0))) & ($greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0))) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & ($greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0))) & ($lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) & ($lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1)) & (~($sum(R!11, $product(-1, J!21)) = 0)))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[133, 132, 127, 123, 119, 118, 114, 113, 109])).
% 0.49/0.57 tff(135,plain,
% 0.49/0.57 (((~$greatereq($sum(I!20, $product(-1, M!12)), 0)) & ((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) & ((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) & (~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0))))) & (~(~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0))))) & (~(~le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))))) & (~(~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0))))) & ($greatereq($sum(I!20, $product(-1, L!13)), 0) & $lesseq($sum(I!20, $product(-1, M!12)), 0) & $greatereq($sum(J!21, $product(-1, M!12)), 0) & $lesseq($sum(J!21, $product(-1, R!11)), 0) & ($sum(I!20, $sum($product(-1, K!18), $sum(J!21, $product(-1, M!12)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)), occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) & (~(~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1)))) & (~($sum(J!21, $product(-1, R!11)) = 0))) <=> ((~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & $greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0)))),
% 0.49/0.57 inference(transitivity,[status(thm)],[134, 108])).
% 0.49/0.57 tff(136,plain,
% 0.49/0.57 ((~(~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)))) <=> ($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(137,plain,
% 0.49/0.57 ((~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $lesseq($sum(L!13, $product(-1, M!12)), 0) & $lesseq($sum(M!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11))) <=> (~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(138,plain,
% 0.49/0.57 ((~(~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $lesseq($sum(L!13, $product(-1, M!12)), 0) & $lesseq($sum(M!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)))) <=> (~(~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11))))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[137])).
% 0.49/0.57 tff(139,plain,
% 0.49/0.57 ((~(~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $lesseq($sum(L!13, $product(-1, M!12)), 0) & $lesseq($sum(M!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)))) <=> ($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11))),
% 0.49/0.57 inference(transitivity,[status(thm)],[138, 136])).
% 0.49/0.57 tff(140,plain,
% 0.49/0.57 ((~(~$greatereq($sum(R!11, $product(-1, L!13)), 1))) <=> $greatereq($sum(R!11, $product(-1, L!13)), 1)),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(141,plain,
% 0.49/0.57 ((~$lesseq($sum(L!13, $product(-1, R!11)), -1)) <=> (~$greatereq($sum(R!11, $product(-1, L!13)), 1))),
% 0.49/0.57 inference(rewrite,[status(thm)],[])).
% 0.49/0.57 tff(142,plain,
% 0.49/0.57 ((~(~$lesseq($sum(L!13, $product(-1, R!11)), -1))) <=> (~(~$greatereq($sum(R!11, $product(-1, L!13)), 1)))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[141])).
% 0.49/0.57 tff(143,plain,
% 0.49/0.57 ((~(~$lesseq($sum(L!13, $product(-1, R!11)), -1))) <=> $greatereq($sum(R!11, $product(-1, L!13)), 1)),
% 0.49/0.57 inference(transitivity,[status(thm)],[142, 140])).
% 0.49/0.57 tff(144,plain,
% 0.49/0.57 (((~(~$lesseq($sum(L!13, $product(-1, R!11)), -1))) & (~(~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $lesseq($sum(L!13, $product(-1, M!12)), 0) & $lesseq($sum(M!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)))) & ((~$greatereq($sum(I!20, $product(-1, M!12)), 0)) & ((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) & ((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) & (~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0))))) & (~(~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0))))) & (~(~le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))))) & (~(~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0))))) & ($greatereq($sum(I!20, $product(-1, L!13)), 0) & $lesseq($sum(I!20, $product(-1, M!12)), 0) & $greatereq($sum(J!21, $product(-1, M!12)), 0) & $lesseq($sum(J!21, $product(-1, R!11)), 0) & ($sum(I!20, $sum($product(-1, K!18), $sum(J!21, $product(-1, M!12)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)), occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) & (~(~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1)))) & (~($sum(J!21, $product(-1, R!11)) = 0)))) <=> ($greatereq($sum(R!11, $product(-1, L!13)), 1) & ($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)) & ((~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & $greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0))))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[143, 139, 135])).
% 0.49/0.57 tff(145,plain,
% 0.49/0.57 (((~(~$lesseq($sum(L!13, $product(-1, R!11)), -1))) & (~(~($greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $lesseq($sum(L!13, $product(-1, M!12)), 0) & $lesseq($sum(M!12, $product(-1, R!11)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11)))) & ((~$greatereq($sum(I!20, $product(-1, M!12)), 0)) & ((~(~($greatereq(A!15, 0) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))))) & ((~(~($sum(I1!23, $product(-1, I!20)) = 1))) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)))) & (~(~($greatereq(A!15, 0) & $greatereq(K!18, 0) & (~$greatereq($sum(K!18, $product(-1, A!15)), 0))))) & (~(~($greatereq(I!20, 0) & (~$greatereq($sum(I!20, $product(-1, Tmp!17)), 0))))) & (~(~le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))))) & (~(~($greatereq(J!21, 0) & (~$greatereq($sum(J!21, $product(-1, Tmp!17)), 0))))) & ($greatereq($sum(I!20, $product(-1, L!13)), 0) & $lesseq($sum(I!20, $product(-1, M!12)), 0) & $greatereq($sum(J!21, $product(-1, M!12)), 0) & $lesseq($sum(J!21, $product(-1, R!11)), 0) & ($sum(I!20, $sum($product(-1, K!18), $sum(J!21, $product(-1, M!12)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$lesseq($sum(K!18, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)), occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1)))))) & (~(~($greatereq($sum(K!18, $product(-1, L!13)), 0) & $lesseq($sum(K!18, $product(-1, R!11)), -1)))) & (~($sum(J!21, $product(-1, R!11)) = 0)))) <=> ($greatereq($sum(R!11, $product(-1, L!13)), 1) & $greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11) & (~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0)))),
% 0.49/0.58 inference(transitivity,[status(thm)],[144, 107])).
% 0.49/0.58 tff(146,plain,
% 0.49/0.58 ((~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ($greatereq($sum(I, $product(-1, M)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp)), 0)))) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Tmp)), 0)))) | (~($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, M)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum($product(-1, K), $sum(J, $product(-1, M)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I)), 0) & (~$greatereq($sum(Y, $product(-1, M)), 0)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J)), 0) & (~$greatereq($sum(Y, $product(-1, R)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L)), 0))) | ($greatereq($sum(I1, $product(-1, R)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($greatereq($sum(K, $product(-1, L)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | ($sum(J, $product(-1, R)) = 0)))) <=> (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ($greatereq($sum(I, $product(-1, M)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp)), 0)))) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Tmp)), 0)))) | (~($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, M)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum($product(-1, K), $sum(J, $product(-1, M)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I)), 0) & (~$greatereq($sum(Y, $product(-1, M)), 0)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J)), 0) & (~$greatereq($sum(Y, $product(-1, R)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L)), 0))) | ($greatereq($sum(I1, $product(-1, R)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($greatereq($sum(K, $product(-1, L)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | ($sum(J, $product(-1, R)) = 0))))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(147,plain,
% 0.49/0.58 ((~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | ($sum(J, $product(-1, R)) = 0) | $lesseq($sum(M, $product(-1, I)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$lesseq($sum(A, $product(-1, K)), 0)))) | (~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (~($greatereq(J, 0) & (~$lesseq($sum(Tmp, $product(-1, J)), 0)))) | (~($lesseq($sum(L, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | (~($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, J)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum(J, $sum($product(-1, M), $product(-1, K)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq($sum(I, $product(-1, Y)), 0) & (~$lesseq($sum(M, $product(-1, Y)), 0)))) | (~($lesseq($sum(L, $product(-1, X)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq($sum(L, $product(-1, X)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($lesseq($sum(J, $product(-1, Y)), 0) & (~$lesseq($sum(R, $product(-1, Y)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$lesseq($sum(L, $product(-1, I1)), 0))) | ($lesseq($sum(R, $product(-1, I1)), 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1)))))))))) <=> (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ($greatereq($sum(I, $product(-1, M)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp)), 0)))) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Tmp)), 0)))) | (~($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, M)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum($product(-1, K), $sum(J, $product(-1, M)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I)), 0) & (~$greatereq($sum(Y, $product(-1, M)), 0)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J)), 0) & (~$greatereq($sum(Y, $product(-1, R)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L)), 0))) | ($greatereq($sum(I1, $product(-1, R)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($greatereq($sum(K, $product(-1, L)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | ($sum(J, $product(-1, R)) = 0))))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(148,plain,
% 0.49/0.58 ((~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))))) <=> (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | ($sum(J, $product(-1, R)) = 0) | $lesseq($sum(M, $product(-1, I)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$lesseq($sum(A, $product(-1, K)), 0)))) | (~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (~($greatereq(J, 0) & (~$lesseq($sum(Tmp, $product(-1, J)), 0)))) | (~($lesseq($sum(L, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | (~($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, J)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum(J, $sum($product(-1, M), $product(-1, K)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq($sum(I, $product(-1, Y)), 0) & (~$lesseq($sum(M, $product(-1, Y)), 0)))) | (~($lesseq($sum(L, $product(-1, X)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq($sum(L, $product(-1, X)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($lesseq($sum(J, $product(-1, Y)), 0) & (~$lesseq($sum(R, $product(-1, Y)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$lesseq($sum(L, $product(-1, I1)), 0))) | ($lesseq($sum(R, $product(-1, I1)), 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))))))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(149,plain,
% 0.49/0.58 ((~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))))) <=> (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R)))))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(150,plain,
% 0.49/0.58 ((~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((((((((($lesseq(0, Tmp) & $lesseq(0, A)) & $lesseq(0, L)) & $lesseq(L, M)) & $lesseq(M, R)) & $lesseq(R, Tmp)) & (Tmp = A)) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M)) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R)) => ($lesseq(L, $difference(R, 1)) => ![J: $int, I: $int, A2: map_int_elt, K: $int] : (($lesseq(L, K) & $lesseq(K, $difference(R, 1))) => (((((((((($lesseq(L, I) & $lesseq(I, M)) & $lesseq(M, J)) & $lesseq(J, R)) & ($difference($sum($difference(I, L), J), M) = $difference(K, L))) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K)) & ![X: $int, Y: $int] : (($lesseq(L, X) & $less(X, K)) => (($lesseq(I, Y) & $less(Y, M)) => le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y))))))) & ![X: $int, Y: $int] : (($lesseq(L, X) & $less(X, K)) => (($lesseq(J, Y) & $less(Y, R)) => le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y))))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K))) & ![I1: $int] : ((($lesseq(0, I1) & $less(I1, L)) | ($lesseq(R, I1) & $less(I1, A))) => (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1)))))) => ($less(I, M) => ((~(J = R)) => (($lesseq(0, J) & $less(J, Tmp)) => (($lesseq(0, I) & $less(I, Tmp)) => (le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J)))) => (($lesseq(0, I) & $less(I, Tmp)) => ((($lesseq(0, A) & $lesseq(0, K)) & $less(K, A)) => ![A3: map_int_elt] : (($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I)))))) => ![I1: $int] : ((I1 = $sum(I, 1)) => ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(K, 1))))))))))))))))) <=> (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R)))))),
% 0.49/0.58 inference(rewrite,[status(thm)],[])).
% 0.49/0.58 tff(151,axiom,(~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((((((((($lesseq(0, Tmp) & $lesseq(0, A)) & $lesseq(0, L)) & $lesseq(L, M)) & $lesseq(M, R)) & $lesseq(R, Tmp)) & (Tmp = A)) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M)) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R)) => ($lesseq(L, $difference(R, 1)) => ![J: $int, I: $int, A2: map_int_elt, K: $int] : (($lesseq(L, K) & $lesseq(K, $difference(R, 1))) => (((((((((($lesseq(L, I) & $lesseq(I, M)) & $lesseq(M, J)) & $lesseq(J, R)) & ($difference($sum($difference(I, L), J), M) = $difference(K, L))) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K)) & ![X: $int, Y: $int] : (($lesseq(L, X) & $less(X, K)) => (($lesseq(I, Y) & $less(Y, M)) => le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y))))))) & ![X: $int, Y: $int] : (($lesseq(L, X) & $less(X, K)) => (($lesseq(J, Y) & $less(Y, R)) => le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y))))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K))) & ![I1: $int] : ((($lesseq(0, I1) & $less(I1, L)) | ($lesseq(R, I1) & $less(I1, A))) => (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1)))))) => ($less(I, M) => ((~(J = R)) => (($lesseq(0, J) & $less(J, Tmp)) => (($lesseq(0, I) & $less(I, Tmp)) => (le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J)))) => (($lesseq(0, I) & $less(I, Tmp)) => ((($lesseq(0, A) & $lesseq(0, K)) & $less(K, A)) => ![A3: map_int_elt] : (($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I)))))) => ![I1: $int] : ((I1 = $sum(I, 1)) => ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(K, 1))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_merge')).
% 0.49/0.58 tff(152,plain,
% 0.49/0.58 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.49/0.59 tff(153,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.49/0.59 tff(154,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.49/0.59 tff(155,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq(L, $sum(-1, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((J = R) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | $lesseq(M, I) | ![A3: map_int_elt] : ((~($lesseq(0, A) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~(I1 = $sum(1, I))) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) | (~($lesseq(0, A) & $lesseq(0, K) & (~$lesseq(A, K)))) | (~($lesseq(0, I) & (~$lesseq(Tmp, I)))) | (~($lesseq(0, J) & (~$lesseq(Tmp, J)))) | (~($lesseq(L, I) & $lesseq(I, M) & $lesseq(M, J) & $lesseq(J, R) & ($sum(I, $sum(J, $product(-1, M))) = K) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(I, Y) & (~$lesseq(M, Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq(L, X) & (~$lesseq(K, X)))) | (~($lesseq(J, Y) & (~$lesseq(R, Y))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J)) = occ1(elt, t2tb2(V), t2tb3(A2), L, K)) & ![I1: $int] : ((~(($lesseq(0, I1) & (~$lesseq(L, I1))) | ($lesseq(R, I1) & (~$lesseq(A, I1))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($lesseq(L, K) & $lesseq(K, $sum(-1, R))))) | (~($lesseq(0, Tmp) & $lesseq(0, A) & $lesseq(0, L) & $lesseq(L, M) & $lesseq(M, R) & $lesseq(R, Tmp) & (Tmp = A) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[154, 149])).
% 0.49/0.59 tff(156,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(Tmp, $product(-1, A)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ((~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | ($sum(J, $product(-1, R)) = 0) | $lesseq($sum(M, $product(-1, I)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$lesseq($sum(A, $product(-1, K)), 0)))) | (~($greatereq(I, 0) & (~$lesseq($sum(Tmp, $product(-1, I)), 0)))) | (~($greatereq(J, 0) & (~$lesseq($sum(Tmp, $product(-1, J)), 0)))) | (~($lesseq($sum(L, $product(-1, K)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | (~($lesseq($sum(L, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, J)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum(J, $sum($product(-1, M), $product(-1, K)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq($sum(I, $product(-1, Y)), 0) & (~$lesseq($sum(M, $product(-1, Y)), 0)))) | (~($lesseq($sum(L, $product(-1, X)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($lesseq($sum(L, $product(-1, X)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($lesseq($sum(J, $product(-1, Y)), 0) & (~$lesseq($sum(R, $product(-1, Y)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$lesseq($sum(L, $product(-1, I1)), 0))) | ($lesseq($sum(R, $product(-1, I1)), 0) & (~$lesseq($sum(A, $product(-1, I1)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1)))))))))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.49/0.59 tff(157,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ($greatereq($sum(I, $product(-1, M)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp)), 0)))) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Tmp)), 0)))) | (~($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, M)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum($product(-1, K), $sum(J, $product(-1, M)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I)), 0) & (~$greatereq($sum(Y, $product(-1, M)), 0)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J)), 0) & (~$greatereq($sum(Y, $product(-1, R)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L)), 0))) | ($greatereq($sum(I1, $product(-1, R)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($greatereq($sum(K, $product(-1, L)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | ($sum(J, $product(-1, R)) = 0)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[156, 147])).
% 0.49/0.59 tff(158,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ($greatereq($sum(I, $product(-1, M)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp)), 0)))) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Tmp)), 0)))) | (~($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, M)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum($product(-1, K), $sum(J, $product(-1, M)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I)), 0) & (~$greatereq($sum(Y, $product(-1, M)), 0)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J)), 0) & (~$greatereq($sum(Y, $product(-1, R)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L)), 0))) | ($greatereq($sum(I1, $product(-1, R)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($greatereq($sum(K, $product(-1, L)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | ($sum(J, $product(-1, R)) = 0)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[157, 146])).
% 0.49/0.59 tff(159,plain,
% 0.49/0.59 (~![Tmp: $int, Tmp1: map_int_elt, A: $int, A1: map_int_elt, L: $int, M: $int, R: $int] : ((~$lesseq($sum(L, $product(-1, R)), -1)) | (~($greatereq(Tmp, 0) & $greatereq(A, 0) & $greatereq(L, 0) & $lesseq($sum(L, $product(-1, M)), 0) & $lesseq($sum(M, $product(-1, R)), 0) & $lesseq($sum(R, $product(-1, Tmp)), 0) & ($sum(A, $product(-1, Tmp)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), L, M) & sorted_sub1(tb2t1(mk_array1(elt, Tmp, t2tb3(Tmp1))), M, R))) | ![J: $int, I: $int, A2: map_int_elt, K: $int] : ($greatereq($sum(I, $product(-1, M)), 0) | ![A3: map_int_elt] : ((~($greatereq(A, 0) & (A3 = tb2t3(set(elt, int, t2tb3(A2), t2tb(K), get(elt, int, t2tb3(Tmp1), t2tb(I))))))) | ![I1: $int] : ((~($sum(I1, $product(-1, I)) = 1)) | ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I1), $product(-1, occ1(elt, t2tb2(V), t2tb3(A3), L, $sum(1, K))))) = 0))) | (~($greatereq(A, 0) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, A)), 0)))) | (~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, Tmp)), 0)))) | (~le1(tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(I))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(J))))) | (~($greatereq(J, 0) & (~$greatereq($sum(J, $product(-1, Tmp)), 0)))) | (~($greatereq($sum(I, $product(-1, L)), 0) & $lesseq($sum(I, $product(-1, M)), 0) & $greatereq($sum(J, $product(-1, M)), 0) & $lesseq($sum(J, $product(-1, R)), 0) & ($sum(I, $sum($product(-1, K), $sum(J, $product(-1, M)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A, t2tb3(A2))), L, K) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I)), 0) & (~$greatereq($sum(Y, $product(-1, M)), 0)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1), t2tb(Y)))) | (~($greatereq($sum(X, $product(-1, L)), 0) & (~$lesseq($sum(K, $product(-1, X)), 0)))) | (~($greatereq($sum(Y, $product(-1, J)), 0) & (~$greatereq($sum(Y, $product(-1, R)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1), L, I), $sum($product(-1, occ1(elt, t2tb2(V), t2tb3(A2), L, K)), occ1(elt, t2tb2(V), t2tb3(Tmp1), M, J))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L)), 0))) | ($greatereq($sum(I1, $product(-1, R)), 0) & (~$greatereq($sum(I1, $product(-1, A)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1), t2tb(I1))))))) | (~($greatereq($sum(K, $product(-1, L)), 0) & $lesseq($sum(K, $product(-1, R)), -1))) | ($sum(J, $product(-1, R)) = 0)))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[158, 146])).
% 0.49/0.59 tff(160,plain,
% 0.49/0.59 ($greatereq($sum(R!11, $product(-1, L!13)), 1) & $greatereq(Tmp!17, 0) & $greatereq(A!15, 0) & $greatereq(L!13, 0) & $greatereq($sum(M!12, $product(-1, L!13)), 0) & $greatereq($sum(R!11, $product(-1, M!12)), 0) & $lesseq($sum(R!11, $product(-1, Tmp!17)), 0) & ($sum(A!15, $product(-1, Tmp!17)) = 0) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), L!13, M!12) & sorted_sub1(tb2t1(mk_array1(elt, Tmp!17, t2tb3(Tmp1!16))), M!12, R!11) & (~$lesseq($sum(M!12, $product(-1, I!20)), 0)) & (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) & ($sum(I!20, $product(-1, I1!23)) = -1) & (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)) & $greatereq(K!18, 0) & (~$lesseq($sum(A!15, $product(-1, K!18)), 0)) & $greatereq(I!20, 0) & (~$lesseq($sum(Tmp!17, $product(-1, I!20)), 0)) & le1(tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(J!21)))) & $greatereq(J!21, 0) & (~$lesseq($sum(Tmp!17, $product(-1, J!21)), 0)) & $lesseq($sum(L!13, $product(-1, I!20)), 0) & $greatereq($sum(M!12, $product(-1, I!20)), 0) & $lesseq($sum(M!12, $product(-1, J!21)), 0) & $greatereq($sum(R!11, $product(-1, J!21)), 0) & ($sum(M!12, $sum(K!18, $sum($product(-1, I!20), $product(-1, J!21)))) = 0) & sorted_sub1(tb2t1(mk_array1(elt, A!15, t2tb3(A2!19))), L!13, K!18) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, I!20)), 0) & (~$greatereq($sum(Y, $product(-1, M!12)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![X: $int, Y: $int] : (le1(tb2t2(get(elt, int, t2tb3(A2!19), t2tb(X))), tb2t2(get(elt, int, t2tb3(Tmp1!16), t2tb(Y)))) | (~($greatereq($sum(Y, $product(-1, J!21)), 0) & (~$greatereq($sum(Y, $product(-1, R!11)), 0)))) | (~($greatereq($sum(X, $product(-1, L!13)), 0) & (~$greatereq($sum(X, $product(-1, K!18)), 0))))) & ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) & ![I1: $int] : ((~(($greatereq(I1, 0) & (~$greatereq($sum(I1, $product(-1, L!13)), 0))) | ($greatereq($sum(I1, $product(-1, R!11)), 0) & (~$greatereq($sum(I1, $product(-1, A!15)), 0))))) | (tb2t2(get(elt, int, t2tb3(A2!19), t2tb(I1))) = tb2t2(get(elt, int, t2tb3(A1!14), t2tb(I1))))) & $lesseq($sum(L!13, $product(-1, K!18)), 0) & $greatereq($sum(R!11, $product(-1, K!18)), 1) & (~($sum(R!11, $product(-1, J!21)) = 0))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[159, 145])).
% 0.49/0.59 tff(161,plain,
% 0.49/0.59 (A3!22 = tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.59 inference(and_elim,[status(thm)],[160])).
% 0.49/0.59 tff(162,plain,
% 0.49/0.59 (t2tb3(A3!22) = t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.59 inference(monotonicity,[status(thm)],[161])).
% 0.49/0.59 tff(163,plain,
% 0.49/0.59 (t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) = t2tb3(A3!22)),
% 0.49/0.59 inference(symmetry,[status(thm)],[162])).
% 0.49/0.59 tff(164,plain,
% 0.49/0.59 (^[A: ty, B: ty, X: uni, X1: uni, X2: uni] : refl(sort1(map(A, B), set(B, A, X, X1, X2)) <=> sort1(map(A, B), set(B, A, X, X1, X2)))),
% 0.49/0.59 inference(bind,[status(th)],[])).
% 0.49/0.59 tff(165,plain,
% 0.49/0.59 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.49/0.59 inference(quant_intro,[status(thm)],[164])).
% 0.49/0.59 tff(166,plain,
% 0.49/0.59 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(167,axiom,(![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_sort2')).
% 0.49/0.59 tff(168,plain,
% 0.49/0.59 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.49/0.59 tff(169,plain,(
% 0.49/0.59 ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.49/0.59 inference(skolemize,[status(sab)],[168])).
% 0.49/0.59 tff(170,plain,
% 0.49/0.59 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))),
% 0.49/0.59 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.49/0.59 tff(171,plain,
% 0.49/0.59 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort1(map(A, B), set(B, A, X, X1, X2))) | sort1(map(int, elt), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.59 inference(quant_inst,[status(thm)],[])).
% 0.49/0.59 tff(172,plain,
% 0.49/0.59 (sort1(map(int, elt), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.59 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.49/0.59 tff(173,plain,
% 0.49/0.59 (^[J: uni] : refl(((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)) <=> ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)))),
% 0.49/0.59 inference(bind,[status(th)],[])).
% 0.49/0.59 tff(174,plain,
% 0.49/0.59 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)) <=> ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.59 inference(quant_intro,[status(thm)],[173])).
% 0.49/0.59 tff(175,plain,
% 0.49/0.59 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)) <=> ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.59 inference(rewrite,[status(thm)],[])).
% 0.49/0.59 tff(176,plain,
% 0.49/0.59 (^[J: uni] : rewrite((sort1(map(int, elt), J) => (t2tb3(tb2t3(J)) = J)) <=> ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J)))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(177,plain,
% 0.49/0.60 (![J: uni] : (sort1(map(int, elt), J) => (t2tb3(tb2t3(J)) = J)) <=> ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[176])).
% 0.49/0.60 tff(178,axiom,(![J: uni] : (sort1(map(int, elt), J) => (t2tb3(tb2t3(J)) = J))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR3')).
% 0.49/0.60 tff(179,plain,
% 0.49/0.60 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.49/0.60 tff(180,plain,
% 0.49/0.60 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.49/0.60 tff(181,plain,(
% 0.49/0.60 ![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.60 inference(skolemize,[status(sab)],[180])).
% 0.49/0.60 tff(182,plain,
% 0.49/0.60 (![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.49/0.60 tff(183,plain,
% 0.49/0.60 (((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) = set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))) <=> ((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) = set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(184,plain,
% 0.49/0.60 ((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | ((~sort1(map(int, elt), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) = set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(185,plain,
% 0.49/0.60 ((~![J: uni] : ((~sort1(map(int, elt), J)) | (t2tb3(tb2t3(J)) = J))) | (~sort1(map(int, elt), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) | (t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) = set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.49/0.60 tff(186,plain,
% 0.49/0.60 (t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) = set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[185, 182, 172])).
% 0.49/0.60 tff(187,plain,
% 0.49/0.60 (set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) = t2tb3(tb2t3(set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.60 inference(symmetry,[status(thm)],[186])).
% 0.49/0.60 tff(188,plain,
% 0.49/0.60 (set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) = t2tb3(A3!22)),
% 0.49/0.60 inference(transitivity,[status(thm)],[187, 163])).
% 0.49/0.60 tff(189,plain,
% 0.49/0.60 (occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))) = occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18)),
% 0.49/0.60 inference(monotonicity,[status(thm)],[188, 102])).
% 0.49/0.60 tff(190,plain,
% 0.49/0.60 (occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18) = occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18)))),
% 0.49/0.60 inference(symmetry,[status(thm)],[189])).
% 0.49/0.60 tff(191,plain,
% 0.49/0.60 ((~(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18) = occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(192,plain,
% 0.49/0.60 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.49/0.60 tff(193,plain,
% 0.49/0.60 ($sum(I!20, $product(-1, I1!23)) = -1),
% 0.49/0.60 inference(and_elim,[status(thm)],[160])).
% 0.49/0.60 tff(194,plain,
% 0.49/0.60 ((~($sum(I!20, $product(-1, I1!23)) = -1)) | $lesseq($sum(I!20, $product(-1, I1!23)), -1)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(195,plain,
% 0.49/0.60 ($lesseq($sum(I!20, $product(-1, I1!23)), -1)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.49/0.60 tff(196,plain,
% 0.49/0.60 ((~($sum(I!20, $product(-1, I1!23)) = -1)) | $greatereq($sum(I!20, $product(-1, I1!23)), -1)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(197,plain,
% 0.49/0.60 ($greatereq($sum(I!20, $product(-1, I1!23)), -1)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[196, 193])).
% 0.49/0.60 tff(198,plain,
% 0.49/0.60 (I!20 = $sum(-1, I1!23)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[197, 195])).
% 0.49/0.60 tff(199,plain,
% 0.49/0.60 ($sum(-1, I1!23) = I!20),
% 0.49/0.60 inference(symmetry,[status(thm)],[198])).
% 0.49/0.60 tff(200,plain,
% 0.49/0.60 (occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)) = occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20)),
% 0.49/0.60 inference(monotonicity,[status(thm)],[199])).
% 0.49/0.60 tff(201,plain,
% 0.49/0.60 (occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20) = occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23))),
% 0.49/0.60 inference(symmetry,[status(thm)],[200])).
% 0.49/0.60 tff(202,plain,
% 0.49/0.60 ((~(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20) = occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(203,plain,
% 0.49/0.60 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.49/0.60 tff(204,plain,
% 0.49/0.60 ($lesseq($sum(L!13, $product(-1, I!20)), 0)),
% 0.49/0.60 inference(and_elim,[status(thm)],[160])).
% 0.49/0.60 tff(205,assumption,($greatereq($sum(L!13, $product(-1, I1!23)), 0)), introduced(assumption)).
% 0.49/0.60 tff(206,plain,
% 0.49/0.60 ($false),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[205, 195, 204])).
% 0.49/0.60 tff(207,plain,(~$greatereq($sum(L!13, $product(-1, I1!23)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.60 tff(208,assumption,(~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)), introduced(assumption)).
% 0.49/0.60 tff(209,plain,
% 0.49/0.60 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1))),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(210,plain,
% 0.49/0.60 (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.49/0.60 tff(211,plain,
% 0.49/0.60 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(212,plain,
% 0.49/0.60 (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.49/0.60 tff(213,plain,
% 0.49/0.60 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.60 tff(214,plain,
% 0.49/0.60 (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[213, 208])).
% 0.49/0.60 tff(215,plain,
% 0.49/0.60 (^[X: elt1] : refl(sort1(elt, t2tb2(X)) <=> sort1(elt, t2tb2(X)))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(216,plain,
% 0.49/0.60 (![X: elt1] : sort1(elt, t2tb2(X)) <=> ![X: elt1] : sort1(elt, t2tb2(X))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[215])).
% 0.49/0.60 tff(217,plain,
% 0.49/0.60 (![X: elt1] : sort1(elt, t2tb2(X)) <=> ![X: elt1] : sort1(elt, t2tb2(X))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(218,axiom,(![X: elt1] : sort1(elt, t2tb2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.49/0.60 tff(219,plain,
% 0.49/0.60 (![X: elt1] : sort1(elt, t2tb2(X))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.49/0.60 tff(220,plain,(
% 0.49/0.60 ![X: elt1] : sort1(elt, t2tb2(X))),
% 0.49/0.60 inference(skolemize,[status(sab)],[219])).
% 0.49/0.60 tff(221,plain,
% 0.49/0.60 (![X: elt1] : sort1(elt, t2tb2(X))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.49/0.60 tff(222,plain,
% 0.49/0.60 ((~![X: elt1] : sort1(elt, t2tb2(X))) | sort1(elt, t2tb2(V!24))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(223,plain,
% 0.49/0.60 (sort1(elt, t2tb2(V!24))),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.49/0.60 tff(224,plain,
% 0.49/0.60 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : refl(($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(225,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[224])).
% 0.49/0.60 tff(226,plain,
% 0.49/0.60 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : trans(monotonicity(trans(monotonicity(rewrite($sum(U, $product(-1, L)) = $sum($product(-1, L), U)), ($lesseq($sum(U, $product(-1, L)), 0) <=> $lesseq($sum($product(-1, L), U), 0))), rewrite($lesseq($sum($product(-1, L), U), 0) <=> $greatereq($sum(L, $product(-1, U)), 0)), ($lesseq($sum(U, $product(-1, L)), 0) <=> $greatereq($sum(L, $product(-1, U)), 0))), (((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)) <=> ((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $greatereq($sum(L, $product(-1, U)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)))), rewrite(((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $greatereq($sum(L, $product(-1, U)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))), (((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(227,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[226])).
% 0.49/0.60 tff(228,plain,
% 0.49/0.60 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : trans(monotonicity(rewrite($lesseq(U, L) <=> $lesseq($sum(U, $product(-1, L)), 0)), rewrite((occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) <=> ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0)), (($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V))) <=> ($lesseq($sum(U, $product(-1, L)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0) | (~sort1(A, V))))), rewrite(($lesseq($sum(U, $product(-1, L)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0) | (~sort1(A, V))) <=> ((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))), (($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V))) <=> ((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(229,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V))) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[228])).
% 0.49/0.60 tff(230,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V))) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V)))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(231,plain,
% 0.49/0.60 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : trans(monotonicity(trans(monotonicity(rewrite($less(L, U) <=> (~$lesseq(U, L))), trans(monotonicity(rewrite((~(get(A, int, M, t2tb($difference(U, 1))) = V)) <=> (~(get(A, int, M, t2tb($sum(-1, U))) = V))), rewrite((occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1))) <=> (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U)))), (((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1)))) <=> ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U)))))), rewrite(((~(get(A, int, M, t2tb($sum(-1, U))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U)))) <=> ((get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))))), (((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1)))) <=> ((get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U)))))), (($less(L, U) => ((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1))))) <=> ((~$lesseq(U, L)) => ((get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))))))), rewrite(((~$lesseq(U, L)) => ((get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))))) <=> ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))))), (($less(L, U) => ((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1))))) <=> ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U)))))), ((sort1(A, V) => ($less(L, U) => ((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1)))))) <=> (sort1(A, V) => ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))))))), rewrite((sort1(A, V) => ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))))) <=> ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V)))), ((sort1(A, V) => ($less(L, U) => ((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1)))))) <=> ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V)))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(232,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : (sort1(A, V) => ($less(L, U) => ((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1)))))) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V)))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[231])).
% 0.49/0.60 tff(233,axiom,(![A: ty, V: uni, M: uni, L: $int, U: $int] : (sort1(A, V) => ($less(L, U) => ((~(get(A, int, M, t2tb($difference(U, 1))) = V)) => (occ1(A, V, M, L, U) = occ1(A, V, M, L, $difference(U, 1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','occ_right_no_add')).
% 0.49/0.60 tff(234,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.49/0.60 tff(235,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (occ1(A, V, M, L, U) = occ1(A, V, M, L, $sum(-1, U))) | (~sort1(A, V)))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.49/0.60 tff(236,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ((get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | $lesseq($sum(U, $product(-1, L)), 0) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[235, 229])).
% 0.49/0.60 tff(237,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[236, 227])).
% 0.49/0.60 tff(238,plain,(
% 0.49/0.60 ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(skolemize,[status(sab)],[237])).
% 0.49/0.60 tff(239,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[238, 225])).
% 0.49/0.60 tff(240,plain,
% 0.49/0.60 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | (~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(241,plain,
% 0.49/0.60 (($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)) <=> ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))),
% 0.49/0.60 inference(rewrite,[status(thm)],[])).
% 0.49/0.60 tff(242,plain,
% 0.49/0.60 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)))),
% 0.49/0.60 inference(monotonicity,[status(thm)],[241])).
% 0.49/0.60 tff(243,plain,
% 0.49/0.60 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | (~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))),
% 0.49/0.60 inference(transitivity,[status(thm)],[242, 240])).
% 0.49/0.60 tff(244,plain,
% 0.49/0.60 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0))),
% 0.49/0.60 inference(quant_inst,[status(thm)],[])).
% 0.49/0.60 tff(245,plain,
% 0.49/0.60 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | (~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)),
% 0.49/0.60 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.49/0.60 tff(246,plain,
% 0.49/0.60 ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[245, 239, 223])).
% 0.49/0.60 tff(247,plain,
% 0.49/0.60 (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)),
% 0.49/0.60 inference(unit_resolution,[status(thm)],[246, 214, 207])).
% 0.49/0.60 tff(248,plain,
% 0.49/0.60 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : refl(($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1)) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1)))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(249,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1)) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))),
% 0.49/0.60 inference(quant_intro,[status(thm)],[248])).
% 0.49/0.60 tff(250,plain,
% 0.49/0.60 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : trans(monotonicity(trans(monotonicity(rewrite($sum(U, $product(-1, L)) = $sum($product(-1, L), U)), ($lesseq($sum(U, $product(-1, L)), 0) <=> $lesseq($sum($product(-1, L), U), 0))), rewrite($lesseq($sum($product(-1, L), U), 0) <=> $greatereq($sum(L, $product(-1, U)), 0)), ($lesseq($sum(U, $product(-1, L)), 0) <=> $greatereq($sum(L, $product(-1, U)), 0))), (((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0)) <=> ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $greatereq($sum(L, $product(-1, U)), 0)))), rewrite(((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $greatereq($sum(L, $product(-1, U)), 0)) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))), (((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0)) <=> ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))))),
% 0.49/0.60 inference(bind,[status(th)],[])).
% 0.49/0.60 tff(251,plain,
% 0.49/0.60 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0)) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[250])).
% 0.49/0.61 tff(252,plain,
% 0.49/0.61 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : trans(monotonicity(rewrite($lesseq(U, L) <=> $lesseq($sum(U, $product(-1, L)), 0)), rewrite((occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))) <=> ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1)), (($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))) <=> ($lesseq($sum(U, $product(-1, L)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1)))), rewrite(($lesseq($sum(U, $product(-1, L)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1)) <=> ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0))), (($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))) <=> ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0))))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(253,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[252])).
% 0.49/0.61 tff(254,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(255,plain,
% 0.49/0.61 (^[A: ty, V: uni, M: uni, L: $int, U: $int] : trans(monotonicity(rewrite($less(L, U) <=> (~$lesseq(U, L))), trans(monotonicity(rewrite((get(A, int, M, t2tb($difference(U, 1))) = V) <=> (get(A, int, M, t2tb($sum(-1, U))) = V)), rewrite((occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1)))) <=> (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))), (((get(A, int, M, t2tb($difference(U, 1))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1))))) <=> ((get(A, int, M, t2tb($sum(-1, U))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))))), rewrite(((get(A, int, M, t2tb($sum(-1, U))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))) <=> ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))), (((get(A, int, M, t2tb($difference(U, 1))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1))))) <=> ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U))))))), (($less(L, U) => ((get(A, int, M, t2tb($difference(U, 1))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1)))))) <=> ((~$lesseq(U, L)) => ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))))), rewrite(((~$lesseq(U, L)) => ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))) <=> ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))), (($less(L, U) => ((get(A, int, M, t2tb($difference(U, 1))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1)))))) <=> ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(256,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($less(L, U) => ((get(A, int, M, t2tb($difference(U, 1))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1)))))) <=> ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[255])).
% 0.49/0.61 tff(257,axiom,(![A: ty, V: uni, M: uni, L: $int, U: $int] : ($less(L, U) => ((get(A, int, M, t2tb($difference(U, 1))) = V) => (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $difference(U, 1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','occ_right_add')).
% 0.49/0.61 tff(258,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.49/0.61 tff(259,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($lesseq(U, L) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | (occ1(A, V, M, L, U) = $sum(1, occ1(A, V, M, L, $sum(-1, U)))))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.49/0.61 tff(260,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ((~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1) | $lesseq($sum(U, $product(-1, L)), 0))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[259, 253])).
% 0.49/0.61 tff(261,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[260, 251])).
% 0.49/0.61 tff(262,plain,(
% 0.49/0.61 ![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))),
% 0.49/0.61 inference(skolemize,[status(sab)],[261])).
% 0.49/0.61 tff(263,plain,
% 0.49/0.61 (![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[262, 249])).
% 0.49/0.61 tff(264,plain,
% 0.49/0.61 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(265,plain,
% 0.49/0.61 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1))),
% 0.49/0.61 inference(quant_inst,[status(thm)],[])).
% 0.49/0.61 tff(266,plain,
% 0.49/0.61 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1)),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.49/0.61 tff(267,plain,
% 0.49/0.61 ($greatereq($sum(L!13, $product(-1, I1!23)), 0) | (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[266, 263])).
% 0.49/0.61 tff(268,plain,
% 0.49/0.61 ($false),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[267, 247, 212, 207])).
% 0.49/0.61 tff(269,plain,($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.61 tff(270,assumption,(~$greatereq($sum(L!13, $product(-1, I1!23)), 0)), introduced(assumption)).
% 0.49/0.61 tff(271,plain,
% 0.49/0.61 ((~(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18) = occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.61 tff(272,plain,
% 0.49/0.61 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[271, 104])).
% 0.49/0.61 tff(273,plain,
% 0.49/0.61 ((~(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18) = occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.61 tff(274,plain,
% 0.49/0.61 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[273, 190])).
% 0.49/0.61 tff(275,assumption,(~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)), introduced(assumption)).
% 0.49/0.61 tff(276,plain,
% 0.49/0.61 ($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[90, 84, 68])).
% 0.49/0.61 tff(277,plain,
% 0.49/0.61 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))) = 0)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.61 tff(278,plain,
% 0.49/0.61 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[277, 276])).
% 0.49/0.61 tff(279,plain,
% 0.49/0.61 ((~(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20) = occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.61 tff(280,plain,
% 0.49/0.61 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[279, 201])).
% 0.49/0.61 tff(281,plain,
% 0.49/0.61 (^[V: elt1] : refl(($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) <=> ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(282,plain,
% 0.49/0.61 (![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0) <=> ![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0)),
% 0.49/0.61 inference(quant_intro,[status(thm)],[281])).
% 0.49/0.61 tff(283,plain,
% 0.49/0.61 (![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0)),
% 0.49/0.61 inference(and_elim,[status(thm)],[160])).
% 0.49/0.61 tff(284,plain,
% 0.49/0.61 (![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0)),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.49/0.61 tff(285,plain,
% 0.49/0.61 ((~![V: elt1] : ($sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V), t2tb3(A2!19), L!13, K!18)))) = 0)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))) = 0)),
% 0.49/0.61 inference(quant_inst,[status(thm)],[])).
% 0.49/0.61 tff(286,plain,
% 0.49/0.61 ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))) = 0),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.49/0.61 tff(287,plain,
% 0.49/0.61 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))) = 0)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)),
% 0.49/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.61 tff(288,plain,
% 0.49/0.61 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[287, 286])).
% 0.49/0.61 tff(289,assumption,(~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))), introduced(assumption)).
% 0.49/0.61 tff(290,plain,
% 0.49/0.61 ($lesseq($sum(L!13, $product(-1, K!18)), 0)),
% 0.49/0.61 inference(and_elim,[status(thm)],[160])).
% 0.49/0.61 tff(291,plain,
% 0.49/0.61 ((~$greatereq($sum(L!13, $product(-1, K!18)), 1)) | (~$lesseq($sum(L!13, $product(-1, K!18)), 0))),
% 0.49/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.61 tff(292,plain,
% 0.49/0.61 (~$greatereq($sum(L!13, $product(-1, K!18)), 1)),
% 0.49/0.61 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.49/0.61 tff(293,plain,
% 0.49/0.61 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | (~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(294,plain,
% 0.49/0.61 (($greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)) <=> ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(295,plain,
% 0.49/0.61 (($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 0) <=> ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(296,plain,
% 0.49/0.61 ((get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24)) <=> (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(297,plain,
% 0.49/0.61 ($greatereq($sum(-1, $sum(L!13, $product(-1, K!18))), 0) <=> $greatereq($sum(L!13, $product(-1, K!18)), 1)),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(298,plain,
% 0.49/0.61 ($sum(L!13, $sum(-1, $product(-1, K!18))) = $sum(-1, $sum(L!13, $product(-1, K!18)))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(299,plain,
% 0.49/0.61 ($sum($product(-1, 1), $product(-1, K!18)) = $sum(-1, $product(-1, K!18))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(300,plain,
% 0.49/0.61 ($product(-1, $sum(1, K!18)) = $sum($product(-1, 1), $product(-1, K!18))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(301,plain,
% 0.49/0.61 ($product(-1, $sum(1, K!18)) = $sum(-1, $product(-1, K!18))),
% 0.49/0.61 inference(transitivity,[status(thm)],[300, 299])).
% 0.49/0.61 tff(302,plain,
% 0.49/0.61 ($sum(L!13, $product(-1, $sum(1, K!18))) = $sum(L!13, $sum(-1, $product(-1, K!18)))),
% 0.49/0.61 inference(monotonicity,[status(thm)],[301])).
% 0.49/0.61 tff(303,plain,
% 0.49/0.61 ($sum(L!13, $product(-1, $sum(1, K!18))) = $sum(-1, $sum(L!13, $product(-1, K!18)))),
% 0.49/0.61 inference(transitivity,[status(thm)],[302, 298])).
% 0.49/0.61 tff(304,plain,
% 0.49/0.61 ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) <=> $greatereq($sum(-1, $sum(L!13, $product(-1, K!18))), 0)),
% 0.49/0.61 inference(monotonicity,[status(thm)],[303])).
% 0.49/0.61 tff(305,plain,
% 0.49/0.61 ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) <=> $greatereq($sum(L!13, $product(-1, K!18)), 1)),
% 0.49/0.61 inference(transitivity,[status(thm)],[304, 297])).
% 0.49/0.61 tff(306,plain,
% 0.49/0.61 (($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 0)) <=> ($greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[305, 296, 295])).
% 0.49/0.62 tff(307,plain,
% 0.49/0.62 (($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 0)) <=> ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0))),
% 0.49/0.62 inference(transitivity,[status(thm)],[306, 294])).
% 0.49/0.62 tff(308,plain,
% 0.49/0.62 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 0))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ((~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[307])).
% 0.49/0.62 tff(309,plain,
% 0.49/0.62 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 0))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | (~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0))),
% 0.49/0.62 inference(transitivity,[status(thm)],[308, 293])).
% 0.49/0.62 tff(310,plain,
% 0.49/0.62 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24)) | (~sort1(elt, t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 0))),
% 0.49/0.62 inference(quant_inst,[status(thm)],[])).
% 0.49/0.62 tff(311,plain,
% 0.49/0.62 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (get(A, int, M, t2tb($sum(-1, U))) = V) | (~sort1(A, V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 0))) | (~sort1(elt, t2tb2(V!24))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.49/0.62 tff(312,plain,
% 0.49/0.62 ((get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[311, 239, 223, 292])).
% 0.49/0.62 tff(313,plain,
% 0.49/0.62 ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[312, 289])).
% 0.49/0.62 tff(314,plain,
% 0.49/0.62 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)),
% 0.49/0.62 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.62 tff(315,plain,
% 0.49/0.62 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.49/0.62 tff(316,plain,
% 0.49/0.62 ((~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0))),
% 0.49/0.62 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.62 tff(317,plain,
% 0.49/0.62 (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[316, 315, 275, 288, 280, 278, 274, 272])).
% 0.49/0.62 tff(318,plain,
% 0.49/0.62 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(319,plain,
% 0.49/0.62 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(320,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.49/0.62 tff(321,plain,
% 0.49/0.62 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.49/0.62 tff(322,plain,(
% 0.49/0.62 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.49/0.62 inference(skolemize,[status(sab)],[321])).
% 0.49/0.62 tff(323,plain,
% 0.49/0.62 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.49/0.62 tff(324,plain,
% 0.49/0.62 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(t2tb(I!20))) = t2tb(I!20))),
% 0.49/0.62 inference(quant_inst,[status(thm)],[])).
% 0.49/0.62 tff(325,plain,
% 0.49/0.62 (t2tb(tb2t(t2tb(I!20))) = t2tb(I!20)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[324, 323])).
% 0.49/0.62 tff(326,plain,
% 0.49/0.62 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(I!20, $product(-1, tb2t(t2tb(I!20)))) = 0)),
% 0.49/0.62 inference(quant_inst,[status(thm)],[])).
% 0.49/0.62 tff(327,plain,
% 0.49/0.62 ($sum(I!20, $product(-1, tb2t(t2tb(I!20)))) = 0),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[326, 62])).
% 0.49/0.62 tff(328,plain,
% 0.49/0.62 ((~($sum(I!20, $product(-1, tb2t(t2tb(I!20)))) = 0)) | $lesseq($sum(I!20, $product(-1, tb2t(t2tb(I!20)))), 0)),
% 0.49/0.62 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.62 tff(329,plain,
% 0.49/0.62 ($lesseq($sum(I!20, $product(-1, tb2t(t2tb(I!20)))), 0)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[328, 327])).
% 0.49/0.62 tff(330,plain,
% 0.49/0.62 ((~($sum(I!20, $product(-1, tb2t(t2tb(I!20)))) = 0)) | $greatereq($sum(I!20, $product(-1, tb2t(t2tb(I!20)))), 0)),
% 0.49/0.62 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.62 tff(331,plain,
% 0.49/0.62 ($greatereq($sum(I!20, $product(-1, tb2t(t2tb(I!20)))), 0)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[330, 327])).
% 0.49/0.62 tff(332,plain,
% 0.49/0.62 (I!20 = tb2t(t2tb(I!20))),
% 0.49/0.62 inference(theory_lemma,[status(thm)],[331, 329])).
% 0.49/0.62 tff(333,plain,
% 0.49/0.62 ($sum(-1, I1!23) = tb2t(t2tb(I!20))),
% 0.49/0.62 inference(transitivity,[status(thm)],[199, 332])).
% 0.49/0.62 tff(334,plain,
% 0.49/0.62 (t2tb($sum(-1, I1!23)) = t2tb(tb2t(t2tb(I!20)))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[333])).
% 0.49/0.62 tff(335,plain,
% 0.49/0.62 (t2tb($sum(-1, I1!23)) = t2tb(I!20)),
% 0.49/0.62 inference(transitivity,[status(thm)],[334, 325])).
% 0.49/0.62 tff(336,plain,
% 0.49/0.62 (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[335])).
% 0.49/0.62 tff(337,plain,
% 0.49/0.62 (get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)) = get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23)))),
% 0.49/0.62 inference(symmetry,[status(thm)],[336])).
% 0.49/0.62 tff(338,plain,
% 0.49/0.62 (^[A: ty, B: ty, X: uni, X1: uni] : refl(sort1(B, get(B, A, X, X1)) <=> sort1(B, get(B, A, X, X1)))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(339,plain,
% 0.49/0.62 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[338])).
% 0.49/0.62 tff(340,plain,
% 0.49/0.62 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(341,axiom,(![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_sort2')).
% 0.49/0.62 tff(342,plain,
% 0.49/0.62 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.49/0.62 tff(343,plain,(
% 0.49/0.62 ![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.49/0.62 inference(skolemize,[status(sab)],[342])).
% 0.49/0.62 tff(344,plain,
% 0.49/0.62 (![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[343, 339])).
% 0.49/0.62 tff(345,plain,
% 0.49/0.62 ((~![A: ty, B: ty, X: uni, X1: uni] : sort1(B, get(B, A, X, X1))) | sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))),
% 0.49/0.62 inference(quant_inst,[status(thm)],[])).
% 0.49/0.62 tff(346,plain,
% 0.49/0.62 (sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[345, 344])).
% 0.49/0.62 tff(347,plain,
% 0.49/0.62 (^[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))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(348,plain,
% 0.49/0.62 (![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)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[347])).
% 0.49/0.62 tff(349,plain,
% 0.49/0.62 (![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)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(350,plain,
% 0.49/0.62 (^[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)))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(351,plain,
% 0.49/0.62 (![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)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[350])).
% 0.49/0.62 tff(352,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/sandbox/benchmark/theBenchmark.p','select_eq')).
% 0.49/0.62 tff(353,plain,
% 0.49/0.62 (![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)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.49/0.62 tff(354,plain,
% 0.49/0.62 (![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)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.49/0.62 tff(355,plain,(
% 0.49/0.62 ![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)))),
% 0.49/0.62 inference(skolemize,[status(sab)],[354])).
% 0.49/0.62 tff(356,plain,
% 0.49/0.62 (![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)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[355, 348])).
% 0.49/0.62 tff(357,plain,
% 0.49/0.62 (((~![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(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) <=> ((~![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(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(358,plain,
% 0.49/0.62 (((get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | $false | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) <=> ((~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(359,plain,
% 0.49/0.62 ((~$true) <=> $false),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(360,plain,
% 0.49/0.62 ((t2tb(K!18) = t2tb(K!18)) <=> $true),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(361,plain,
% 0.49/0.62 ((~(t2tb(K!18) = t2tb(K!18))) <=> (~$true)),
% 0.49/0.62 inference(monotonicity,[status(thm)],[360])).
% 0.49/0.62 tff(362,plain,
% 0.49/0.62 ((~(t2tb(K!18) = t2tb(K!18))) <=> $false),
% 0.49/0.62 inference(transitivity,[status(thm)],[361, 359])).
% 0.49/0.62 tff(363,plain,
% 0.49/0.62 (((get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | (~(t2tb(K!18) = t2tb(K!18))) | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) <=> ((get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | $false | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[362])).
% 0.49/0.62 tff(364,plain,
% 0.49/0.62 (((get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | (~(t2tb(K!18) = t2tb(K!18))) | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))) <=> ((~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.62 inference(transitivity,[status(thm)],[363, 358])).
% 0.49/0.62 tff(365,plain,
% 0.49/0.62 (((~![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(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | (~(t2tb(K!18) = t2tb(K!18))) | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))) <=> ((~![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(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[364])).
% 0.49/0.63 tff(366,plain,
% 0.49/0.63 (((~![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(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | (~(t2tb(K!18) = t2tb(K!18))) | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))) <=> ((~![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(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[365, 357])).
% 0.49/0.63 tff(367,plain,
% 0.49/0.63 ((~![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(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))) | (~(t2tb(K!18) = t2tb(K!18))) | (~sort1(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))))),
% 0.49/0.63 inference(quant_inst,[status(thm)],[])).
% 0.49/0.63 tff(368,plain,
% 0.49/0.63 ((~![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(elt, get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))) | (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.49/0.63 tff(369,plain,
% 0.49/0.63 (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[368, 356, 346])).
% 0.49/0.63 tff(370,plain,
% 0.49/0.63 (t2tb3(A3!22) = set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[162, 186])).
% 0.49/0.63 tff(371,plain,
% 0.49/0.63 (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[370])).
% 0.49/0.63 tff(372,plain,
% 0.49/0.63 (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[371, 369, 337])).
% 0.49/0.63 tff(373,plain,
% 0.49/0.63 ((get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) <=> (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[372])).
% 0.49/0.63 tff(374,plain,
% 0.49/0.63 ((~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) <=> (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[373])).
% 0.49/0.63 tff(375,plain,
% 0.49/0.63 (~(get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[289, 374])).
% 0.49/0.63 tff(376,plain,
% 0.49/0.63 ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[246, 375, 270])).
% 0.49/0.63 tff(377,plain,
% 0.49/0.63 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(378,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[377, 376, 317])).
% 0.49/0.63 tff(379,plain,((get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)) | $greatereq($sum(L!13, $product(-1, I1!23)), 0) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.63 tff(380,plain,
% 0.49/0.63 (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[379, 270, 275])).
% 0.49/0.63 tff(381,plain,
% 0.49/0.63 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(382,plain,
% 0.49/0.63 (($greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)) <=> ($greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(383,plain,
% 0.49/0.63 (($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 1) <=> ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(384,plain,
% 0.49/0.63 ((~(get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24))) <=> (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(385,plain,
% 0.49/0.63 (($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (~(get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 1)) <=> ($greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[305, 384, 383])).
% 0.49/0.63 tff(386,plain,
% 0.49/0.63 (($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (~(get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 1)) <=> ($greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1))),
% 0.49/0.63 inference(transitivity,[status(thm)],[385, 382])).
% 0.49/0.63 tff(387,plain,
% 0.49/0.63 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (~(get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 1))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[386])).
% 0.49/0.63 tff(388,plain,
% 0.49/0.63 (((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (~(get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 1))) <=> ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1))),
% 0.49/0.63 inference(transitivity,[status(thm)],[387, 381])).
% 0.49/0.63 tff(389,plain,
% 0.49/0.63 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | ($greatereq($sum(L!13, $product(-1, $sum(1, K!18))), 0) | (~(get(elt, int, t2tb3(A3!22), t2tb($sum(-1, $sum(1, K!18)))) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(-1, $sum(1, K!18))))) = 1))),
% 0.49/0.63 inference(quant_inst,[status(thm)],[])).
% 0.49/0.63 tff(390,plain,
% 0.49/0.63 ((~![A: ty, V: uni, M: uni, L: $int, U: $int] : ($greatereq($sum(L, $product(-1, U)), 0) | (~(get(A, int, M, t2tb($sum(-1, U))) = V)) | ($sum(occ1(A, V, M, L, U), $product(-1, occ1(A, V, M, L, $sum(-1, U)))) = 1))) | $greatereq($sum(L!13, $product(-1, K!18)), 1) | (~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.49/0.63 tff(391,plain,
% 0.49/0.63 ((~(get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24))) | ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[390, 263, 292])).
% 0.49/0.63 tff(392,plain,
% 0.49/0.63 ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[391, 380])).
% 0.49/0.63 tff(393,plain,
% 0.49/0.63 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1)),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(394,plain,
% 0.49/0.63 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[393, 392])).
% 0.49/0.63 tff(395,plain,
% 0.49/0.63 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1))),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(396,plain,
% 0.49/0.63 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[395, 394])).
% 0.49/0.63 tff(397,plain,
% 0.49/0.63 (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[316, 278, 275, 288, 280, 396, 274, 272])).
% 0.49/0.63 tff(398,plain,
% 0.49/0.63 (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[377, 397])).
% 0.49/0.63 tff(399,plain,
% 0.49/0.63 (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[246, 398, 270])).
% 0.49/0.63 tff(400,plain,
% 0.49/0.63 ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[267, 399, 270])).
% 0.49/0.63 tff(401,plain,
% 0.49/0.63 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1)),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(402,plain,
% 0.49/0.63 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[401, 400])).
% 0.49/0.63 tff(403,plain,
% 0.49/0.63 ((~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1))),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(404,plain,
% 0.49/0.63 (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[403, 394])).
% 0.49/0.63 tff(405,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[280, 288, 274, 404, 275, 278, 272, 402])).
% 0.49/0.63 tff(406,plain,($greatereq($sum(L!13, $product(-1, I1!23)), 0) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.63 tff(407,plain,
% 0.49/0.63 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[406, 207])).
% 0.49/0.63 tff(408,plain,
% 0.49/0.63 (~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0)),
% 0.49/0.63 inference(and_elim,[status(thm)],[160])).
% 0.49/0.63 tff(409,plain,
% 0.49/0.63 (($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))) = 0) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0))),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(410,plain,
% 0.49/0.63 ((~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[409, 408])).
% 0.49/0.63 tff(411,plain,
% 0.49/0.63 (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[410, 407])).
% 0.49/0.63 tff(412,plain,
% 0.49/0.63 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))) = 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)),
% 0.49/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.63 tff(413,plain,
% 0.49/0.63 ($greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[412, 286])).
% 0.49/0.63 tff(414,plain,
% 0.49/0.63 ((~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0))),
% 0.49/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.64 tff(415,plain,
% 0.49/0.64 ((~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0))),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[414, 192, 203, 106, 413])).
% 0.49/0.64 tff(416,plain,
% 0.49/0.64 (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[415, 94, 411, 269])).
% 0.49/0.64 tff(417,plain,
% 0.49/0.64 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 0)),
% 0.49/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.64 tff(418,plain,
% 0.49/0.64 (~($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 0)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[417, 416])).
% 0.49/0.64 tff(419,plain,
% 0.49/0.64 (get(elt, int, t2tb3(A3!22), t2tb(K!18)) = t2tb2(V!24)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[312, 418])).
% 0.49/0.64 tff(420,plain,
% 0.49/0.64 ($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[391, 419])).
% 0.49/0.64 tff(421,plain,
% 0.49/0.64 ((~($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))) = 1)) | $lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1)),
% 0.49/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.49/0.64 tff(422,plain,
% 0.49/0.64 ($lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1)),
% 0.49/0.64 inference(unit_resolution,[status(thm)],[421, 420])).
% 0.49/0.64 tff(423,plain,
% 0.49/0.64 ((~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18)))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18)), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, K!18))), 1)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))), $product(-1, occ1(elt, t2tb2(V!24), set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), L!13, tb2t(t2tb(K!18))))), 0)) | (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, K!18), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A2!19), L!13, tb2t(t2tb(K!18))))), 0)) | (~$lesseq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I!20), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 0)) | $greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), M!12, J!21), $sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(A3!22), L!13, $sum(1, K!18))))), 0)),
% 0.57/0.65 inference(theory_lemma,[status(thm)],[])).
% 0.57/0.65 tff(424,plain,
% 0.57/0.65 (~$greatereq($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))), 1)),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[423, 413, 411, 422, 203, 192, 106, 94])).
% 0.57/0.65 tff(425,plain,
% 0.57/0.65 (get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18)) = get(elt, int, t2tb3(A3!22), t2tb(K!18))),
% 0.57/0.65 inference(monotonicity,[status(thm)],[188])).
% 0.57/0.65 tff(426,plain,
% 0.57/0.65 (get(elt, int, t2tb3(Tmp1!16), t2tb(I!20)) = get(elt, int, set(elt, int, t2tb3(A2!19), t2tb(K!18), get(elt, int, t2tb3(Tmp1!16), t2tb(I!20))), t2tb(K!18))),
% 0.57/0.65 inference(symmetry,[status(thm)],[369])).
% 0.57/0.65 tff(427,plain,
% 0.57/0.65 (get(elt, int, t2tb3(Tmp1!16), t2tb($sum(-1, I1!23))) = t2tb2(V!24)),
% 0.57/0.65 inference(transitivity,[status(thm)],[336, 426, 425, 419])).
% 0.57/0.65 tff(428,plain,
% 0.57/0.65 ($sum(occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, I1!23), $product(-1, occ1(elt, t2tb2(V!24), t2tb3(Tmp1!16), L!13, $sum(-1, I1!23)))) = 1),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[267, 427, 207])).
% 0.57/0.65 tff(429,plain,
% 0.57/0.65 ($false),
% 0.57/0.65 inference(unit_resolution,[status(thm)],[211, 428, 424])).
% 0.57/0.65 % SZS output end Proof
%------------------------------------------------------------------------------