TSTP Solution File: SWW596_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW596_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:23 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW596_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 20:14:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(nb_occ_type, type, (
% 0.19/0.49 nb_occ: ( map_int_color * $int * $int * color ) > $int)).
% 0.19/0.49 tff(tptp_fun_C_7_type, type, (
% 0.19/0.49 tptp_fun_C_7: color)).
% 0.19/0.49 tff(tptp_fun_K2_8_type, type, (
% 0.19/0.49 tptp_fun_K2_8: $int)).
% 0.19/0.49 tff(tptp_fun_K1_9_type, type, (
% 0.19/0.49 tptp_fun_K1_9: $int)).
% 0.19/0.49 tff(tptp_fun_A_5_type, type, (
% 0.19/0.49 tptp_fun_A_5: map_int_color)).
% 0.19/0.49 tff(tptp_fun_A2_6_type, type, (
% 0.19/0.49 tptp_fun_A2_6: map_int_color)).
% 0.19/0.49 tff(tb2t1_type, type, (
% 0.19/0.49 tb2t1: uni > color)).
% 0.19/0.49 tff(get_type, type, (
% 0.19/0.49 get: ( ty * ty * uni * uni ) > uni)).
% 0.19/0.49 tff(t2tb2_type, type, (
% 0.19/0.49 t2tb2: $int > uni)).
% 0.19/0.49 tff(tptp_fun_J_3_type, type, (
% 0.19/0.49 tptp_fun_J_3: $int)).
% 0.19/0.49 tff(t2tb_type, type, (
% 0.19/0.49 t2tb: map_int_color > uni)).
% 0.19/0.49 tff(int_type, type, (
% 0.19/0.49 int: ty)).
% 0.19/0.49 tff(color1_type, type, (
% 0.19/0.49 color1: ty)).
% 0.19/0.49 tff(tb2t_type, type, (
% 0.19/0.49 tb2t: uni > map_int_color)).
% 0.19/0.49 tff(set_type, type, (
% 0.19/0.49 set: ( ty * ty * uni * uni * uni ) > uni)).
% 0.19/0.49 tff(t2tb1_type, type, (
% 0.19/0.49 t2tb1: color > uni)).
% 0.19/0.49 tff(tb2t2_type, type, (
% 0.19/0.49 tb2t2: uni > $int)).
% 0.19/0.49 tff(tptp_fun_I_4_type, type, (
% 0.19/0.49 tptp_fun_I_4: $int)).
% 0.19/0.49 tff(sort_type, type, (
% 0.19/0.49 sort: ( ty * uni ) > $o)).
% 0.19/0.49 tff(map_type, type, (
% 0.19/0.49 map: ( ty * ty ) > ty)).
% 0.19/0.49 tff(tptp_fun_A1_2_type, type, (
% 0.19/0.49 tptp_fun_A1_2: map_int_color)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 (^[A: ty, B: ty, X: uni, X1: uni] : refl(sort(B, get(B, A, X, X1)) <=> sort(B, get(B, A, X, X1)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(2,plain,
% 0.19/0.49 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.49 tff(3,plain,
% 0.19/0.49 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1)) <=> ![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(4,axiom,(![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','get_sort')).
% 0.19/0.49 tff(5,plain,
% 0.19/0.49 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.49 tff(6,plain,(
% 0.19/0.49 ![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 0.19/0.49 inference(skolemize,[status(sab)],[5])).
% 0.19/0.49 tff(7,plain,
% 0.19/0.49 (![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.49 tff(8,plain,
% 0.19/0.49 ((~![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))) | sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(9,plain,
% 0.19/0.49 (sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (^[J: uni] : refl(((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J)) <=> ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(11,plain,
% 0.19/0.49 (![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J)) <=> ![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.49 tff(12,plain,
% 0.19/0.49 (![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J)) <=> ![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(13,plain,
% 0.19/0.49 (^[J: uni] : rewrite((sort(color1, J) => (t2tb1(tb2t1(J)) = J)) <=> ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 (![J: uni] : (sort(color1, J) => (t2tb1(tb2t1(J)) = J)) <=> ![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.49 tff(15,axiom,(![J: uni] : (sort(color1, J) => (t2tb1(tb2t1(J)) = J))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.19/0.49 tff(16,plain,
% 0.19/0.49 (![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.49 tff(17,plain,
% 0.19/0.49 (![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.49 tff(18,plain,(
% 0.19/0.49 ![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.49 inference(skolemize,[status(sab)],[17])).
% 0.19/0.49 tff(19,plain,
% 0.19/0.49 (![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(J!3))))) <=> ((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 ((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 ((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(J!3))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.50 tff(24,assumption,(~(get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3)))), introduced(assumption)).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (^[X: $int] : refl(sort(int, t2tb2(X)) <=> sort(int, t2tb2(X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (![X: $int] : sort(int, t2tb2(X)) <=> ![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (![X: $int] : sort(int, t2tb2(X)) <=> ![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(28,axiom,(![X: $int] : sort(int, t2tb2(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.50 tff(30,plain,(
% 0.19/0.50 ![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[29])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 ((~![X: $int] : sort(int, t2tb2(X))) | sort(int, t2tb2(J!3))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (sort(int, t2tb2(J!3))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 ((~![X: $int] : sort(int, t2tb2(X))) | sort(int, t2tb2(I!4))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (sort(int, t2tb2(I!4))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite(((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : refl(((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : rewrite(((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1))) <=> ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (^[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))))), ((sort(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> (sort(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), rewrite((sort(A, A2) => ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((sort(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))) <=> ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2)))))), ((sort(A, A1) => (sort(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> (sort(A, A1) => ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))))), rewrite((sort(A, A1) => ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))), ((sort(A, A1) => (sort(A, A2) => ![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) <=> ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort(A, A1) => (sort(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] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.50 tff(46,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni] : (sort(A, A1) => (sort(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')).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.50 tff(49,plain,(
% 0.19/0.50 ![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[48])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) | (~sort(A, A1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[50, 37])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort(int, t2tb2(J!3))) | (~sort(int, t2tb2(I!4))) | ![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3)))))) <=> ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort(int, t2tb2(J!3))) | (~sort(int, t2tb2(I!4))) | ![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | ((~sort(int, t2tb2(J!3))) | (~sort(int, t2tb2(I!4))) | ![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni] : ((~sort(A, A2)) | (~sort(A, A1)) | ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))) | (~sort(int, t2tb2(J!3))) | (~sort(int, t2tb2(I!4))) | ![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[54, 51, 35, 33])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (((~![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))) <=> ((~![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))) | (t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 ((~![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 ((~![B1: uni] : ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), B1), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))))) | (t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.50 tff(59,plain,
% 0.19/0.50 ((t2tb2(I!4) = t2tb2(J!3)) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 (t2tb2(I!4) = t2tb2(J!3)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[59, 24])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : refl(((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1))) <=> ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(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)) | (~sort(B, B1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(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)) | (~sort(B, B1)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : trans(monotonicity(rewrite(((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)) <=> ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))), ((sort(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1))) <=> (sort(B, B1) => ((~(A1 = A2)) | (get(B, A, set(B, A, M, A1, B1), A2) = B1))))), rewrite((sort(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)) | (~sort(B, B1)))), ((sort(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)) | (~sort(B, B1)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort(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)) | (~sort(B, B1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.50 tff(66,axiom,(![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : (sort(B, B1) => ((A1 = A2) => (get(B, A, set(B, A, M, A1, B1), A2) = B1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','select_eq')).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.50 tff(69,plain,(
% 0.19/0.50 ![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[68])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 (![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))))) <=> ((~![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)) | (~sort(B, B1)))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (((get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3))))) <=> ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))))) <=> ((~![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)) | (~sort(B, B1)))) | ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))))) <=> ((~![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)) | (~sort(B, B1)))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | ((get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 ((~![A: ty, B: ty, M: uni, A1: uni, A2: uni, B1: uni] : ((get(B, A, set(B, A, M, A1, B1), A2) = B1) | (~(A1 = A2)) | (~sort(B, B1)))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 ((get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))) | (~(t2tb2(I!4) = t2tb2(J!3)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[76, 70, 9])).
% 0.19/0.51 tff(78,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[77, 60, 24])).
% 0.19/0.51 tff(79,plain,(get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3)) = get(color1, int, t2tb(A!5), t2tb2(J!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 (![J: uni] : (t2tb2(tb2t2(J)) = J) <=> ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(82,axiom,(![J: uni] : (t2tb2(tb2t2(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR2')).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.51 tff(84,plain,(
% 0.19/0.51 ![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.19/0.51 inference(skolemize,[status(sab)],[83])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 (![J: uni] : (t2tb2(tb2t2(J)) = J)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.51 tff(86,plain,
% 0.19/0.51 ((~![J: uni] : (t2tb2(tb2t2(J)) = J)) | (t2tb2(tb2t2(t2tb2(J!3))) = t2tb2(J!3))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 (t2tb2(tb2t2(t2tb2(J!3))) = t2tb2(J!3)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.51 tff(88,plain,
% 0.19/0.51 (^[A: ty, B: ty, X: uni, X1: uni, X2: uni] : refl(sort(map(A, B), set(B, A, X, X1, X2)) <=> sort(map(A, B), set(B, A, X, X1, X2)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2)) <=> ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(91,axiom,(![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','set_sort')).
% 0.19/0.51 tff(92,plain,
% 0.19/0.51 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.51 tff(93,plain,(
% 0.19/0.51 ![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 0.19/0.51 inference(skolemize,[status(sab)],[92])).
% 0.19/0.51 tff(94,plain,
% 0.19/0.51 (![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.51 tff(95,plain,
% 0.19/0.51 ((~![A: ty, B: ty, X: uni, X1: uni, X2: uni] : sort(map(A, B), set(B, A, X, X1, X2))) | sort(map(int, color1), set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(96,plain,
% 0.19/0.51 (sort(map(int, color1), set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.51 tff(97,plain,
% 0.19/0.51 (^[J: uni] : refl(((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J)) <=> ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(98,plain,
% 0.19/0.51 (![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J)) <=> ![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.51 tff(99,plain,
% 0.19/0.51 (![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J)) <=> ![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(100,plain,
% 0.19/0.51 (^[J: uni] : rewrite((sort(map(int, color1), J) => (t2tb(tb2t(J)) = J)) <=> ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(101,plain,
% 0.19/0.51 (![J: uni] : (sort(map(int, color1), J) => (t2tb(tb2t(J)) = J)) <=> ![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.51 tff(102,axiom,(![J: uni] : (sort(map(int, color1), J) => (t2tb(tb2t(J)) = J))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.19/0.51 tff(103,plain,
% 0.19/0.51 (![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.51 tff(104,plain,
% 0.19/0.51 (![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.51 tff(105,plain,(
% 0.19/0.51 ![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(skolemize,[status(sab)],[104])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 (![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.19/0.51 tff(107,plain,
% 0.19/0.51 (((~![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))) | ((~sort(map(int, color1), set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) | (t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))))) <=> ((~![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))) | (~sort(map(int, color1), set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) | (t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 ((~![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))) | ((~sort(map(int, color1), set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) | (t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 ((~![J: uni] : ((~sort(map(int, color1), J)) | (t2tb(tb2t(J)) = J))) | (~sort(map(int, color1), set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) | (t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 (t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[109, 106, 96])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 (get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3)))) = get(color1, int, set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))), t2tb2(J!3))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[110, 87])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(J!3))),
% 0.19/0.51 inference(transitivity,[status(thm)],[111, 79])).
% 0.19/0.51 tff(113,plain,
% 0.19/0.51 (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.51 tff(114,assumption,(~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)), introduced(assumption)).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = C!7) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.19/0.51 inference(commutativity,[status(thm)],[])).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 ((~![J: uni] : (t2tb2(tb2t2(J)) = J)) | (t2tb2(tb2t2(t2tb2(I!4))) = t2tb2(I!4))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 (t2tb2(tb2t2(t2tb2(I!4))) = t2tb2(I!4)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[116, 85])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 (get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(I!4))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = C!7)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[119])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[120, 115])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7)),
% 0.19/0.51 inference(symmetry,[status(thm)],[121])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 ((~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) <=> (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.51 tff(124,assumption,(~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))), introduced(assumption)).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))) = C!7) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.51 inference(commutativity,[status(thm)],[])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))) = C!7)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[113])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[127, 126])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 ((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) <=> (~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 (~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[114, 129])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 (((A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) & ((A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))) & (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))))) <=> ((A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) & (A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))) & (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(132,plain,
% 0.19/0.51 (((~(~(A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))))) & (~((~($lesseq($sum(K1!9, $product(-1, I!4)), 0) & (~$lesseq($sum(K2!8, $product(-1, I!4)), 0)) & $lesseq($sum(K1!9, $product(-1, J!3)), 0) & (~$lesseq($sum(K2!8, $product(-1, J!3)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0)))) <=> ((A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))) & (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(133,plain,
% 0.19/0.51 ((~(~(A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))))) <=> (A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(134,plain,
% 0.19/0.51 (((~(~(A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))))) & ((~(~(A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))))) & (~((~($lesseq($sum(K1!9, $product(-1, I!4)), 0) & (~$lesseq($sum(K2!8, $product(-1, I!4)), 0)) & $lesseq($sum(K1!9, $product(-1, J!3)), 0) & (~$lesseq($sum(K2!8, $product(-1, J!3)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))))) <=> ((A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) & ((A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))) & (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[133, 132])).
% 0.19/0.51 tff(135,plain,
% 0.19/0.51 (((~(~(A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))))) & ((~(~(A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))))) & (~((~($lesseq($sum(K1!9, $product(-1, I!4)), 0) & (~$lesseq($sum(K2!8, $product(-1, I!4)), 0)) & $lesseq($sum(K1!9, $product(-1, J!3)), 0) & (~$lesseq($sum(K2!8, $product(-1, J!3)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))))) <=> ((A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) & (A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))) & (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[134, 131])).
% 0.19/0.51 tff(136,plain,
% 0.19/0.51 ((~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq($sum(K1, $product(-1, I)), 0) & (~$lesseq($sum(K2, $product(-1, I)), 0)) & $lesseq($sum(K1, $product(-1, J)), 0) & (~$lesseq($sum(K2, $product(-1, J)), 0)))) | ($sum(nb_occ(A2, K1, K2, C), $product(-1, nb_occ(A, K1, K2, C))) = 0))))) <=> (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq($sum(K1, $product(-1, I)), 0) & (~$lesseq($sum(K2, $product(-1, I)), 0)) & $lesseq($sum(K1, $product(-1, J)), 0) & (~$lesseq($sum(K2, $product(-1, J)), 0)))) | ($sum(nb_occ(A2, K1, K2, C), $product(-1, nb_occ(A, K1, K2, C))) = 0)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 ((~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))) <=> (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq($sum(K1, $product(-1, I)), 0) & (~$lesseq($sum(K2, $product(-1, I)), 0)) & $lesseq($sum(K1, $product(-1, J)), 0) & (~$lesseq($sum(K2, $product(-1, J)), 0)))) | ($sum(nb_occ(A2, K1, K2, C), $product(-1, nb_occ(A, K1, K2, C))) = 0)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 ((~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))) <=> (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 ((~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J))))) => ![A2: map_int_color] : ((A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I))))) => ![K1: $int, K2: $int, C: color] : (((($lesseq(K1, I) & $less(I, K2)) & $lesseq(K1, J)) & $less(J, K2)) => (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))) <=> (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(140,axiom,(~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J))))) => ![A2: map_int_color] : ((A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I))))) => ![K1: $int, K2: $int, C: color] : (((($lesseq(K1, I) & $less(I, K2)) & $lesseq(K1, J)) & $less(J, K2)) => (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_swap')).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.52 tff(142,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[141, 138])).
% 0.19/0.52 tff(143,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.19/0.52 tff(144,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq(K1, I) & (~$lesseq(K2, I)) & $lesseq(K1, J) & (~$lesseq(K2, J)))) | (nb_occ(A2, K1, K2, C) = nb_occ(A, K1, K2, C)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[143, 138])).
% 0.19/0.52 tff(145,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq($sum(K1, $product(-1, I)), 0) & (~$lesseq($sum(K2, $product(-1, I)), 0)) & $lesseq($sum(K1, $product(-1, J)), 0) & (~$lesseq($sum(K2, $product(-1, J)), 0)))) | ($sum(nb_occ(A2, K1, K2, C), $product(-1, nb_occ(A, K1, K2, C))) = 0))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.19/0.52 tff(146,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq($sum(K1, $product(-1, I)), 0) & (~$lesseq($sum(K2, $product(-1, I)), 0)) & $lesseq($sum(K1, $product(-1, J)), 0) & (~$lesseq($sum(K2, $product(-1, J)), 0)))) | ($sum(nb_occ(A2, K1, K2, C), $product(-1, nb_occ(A, K1, K2, C))) = 0))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[145, 136])).
% 0.19/0.52 tff(147,plain,
% 0.19/0.52 (~![A: map_int_color, I: $int, J: $int, A1: map_int_color] : ((~(A1 = tb2t(set(color1, int, t2tb(A), t2tb2(I), get(color1, int, t2tb(A), t2tb2(J)))))) | ![A2: map_int_color] : ((~(A2 = tb2t(set(color1, int, t2tb(A1), t2tb2(J), get(color1, int, t2tb(A), t2tb2(I)))))) | ![K1: $int, K2: $int, C: color] : ((~($lesseq($sum(K1, $product(-1, I)), 0) & (~$lesseq($sum(K2, $product(-1, I)), 0)) & $lesseq($sum(K1, $product(-1, J)), 0) & (~$lesseq($sum(K2, $product(-1, J)), 0)))) | ($sum(nb_occ(A2, K1, K2, C), $product(-1, nb_occ(A, K1, K2, C))) = 0))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.19/0.52 tff(148,plain,
% 0.19/0.52 ((A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) & (A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))) & (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[147, 135])).
% 0.19/0.52 tff(149,plain,
% 0.19/0.52 (~((~($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)))) | ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0))),
% 0.19/0.52 inference(and_elim,[status(thm)],[148])).
% 0.19/0.52 tff(150,plain,
% 0.19/0.52 ($greatereq($sum(I!4, $product(-1, K1!9)), 0) & (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)) & $greatereq($sum(J!3, $product(-1, K1!9)), 0) & (~$greatereq($sum(J!3, $product(-1, K2!8)), 0))),
% 0.19/0.52 inference(or_elim,[status(thm)],[149])).
% 0.19/0.52 tff(151,plain,
% 0.19/0.52 (~$greatereq($sum(I!4, $product(-1, K2!8)), 0)),
% 0.19/0.52 inference(and_elim,[status(thm)],[150])).
% 0.19/0.52 tff(152,plain,
% 0.19/0.52 (^[I: $int] : refl(($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(153,plain,
% 0.19/0.52 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.52 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.52 tff(154,plain,
% 0.19/0.52 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t2(t2tb2(I)), $product(-1, I)) = $sum($product(-1, I), tb2t2(t2tb2(I)))), (($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t2(t2tb2(I))) = 0))), rewrite(($sum($product(-1, I), tb2t2(t2tb2(I))) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)), (($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(155,plain,
% 0.19/0.52 (![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.52 inference(quant_intro,[status(thm)],[154])).
% 0.19/0.52 tff(156,plain,
% 0.19/0.52 (^[I: $int] : rewrite((tb2t2(t2tb2(I)) = I) <=> ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(157,plain,
% 0.19/0.52 (![I: $int] : (tb2t2(t2tb2(I)) = I) <=> ![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0)),
% 0.19/0.52 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.52 tff(158,plain,
% 0.19/0.52 (![I: $int] : (tb2t2(t2tb2(I)) = I) <=> ![I: $int] : (tb2t2(t2tb2(I)) = I)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(159,axiom,(![I: $int] : (tb2t2(t2tb2(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL2')).
% 0.19/0.52 tff(160,plain,
% 0.19/0.52 (![I: $int] : (tb2t2(t2tb2(I)) = I)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.52 tff(161,plain,
% 0.19/0.52 (![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[160, 157])).
% 0.19/0.52 tff(162,plain,
% 0.19/0.52 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[161, 155])).
% 0.19/0.52 tff(163,plain,(
% 0.19/0.52 ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.52 inference(skolemize,[status(sab)],[162])).
% 0.19/0.52 tff(164,plain,
% 0.19/0.52 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[163, 153])).
% 0.19/0.52 tff(165,plain,
% 0.19/0.52 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))) = 0)),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(166,plain,
% 0.19/0.52 ($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))) = 0),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.52 tff(167,plain,
% 0.19/0.52 ((~($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))) = 0)) | $greatereq($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(168,plain,
% 0.19/0.52 ($greatereq($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.52 tff(169,assumption,($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0)), introduced(assumption)).
% 0.19/0.52 tff(170,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[169, 168, 151])).
% 0.19/0.52 tff(171,plain,(~$lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(172,plain,
% 0.19/0.52 ($greatereq($sum(I!4, $product(-1, K1!9)), 0)),
% 0.19/0.52 inference(and_elim,[status(thm)],[150])).
% 0.19/0.52 tff(173,assumption,(~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)), introduced(assumption)).
% 0.19/0.52 tff(174,plain,
% 0.19/0.52 ((~($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))) = 0)) | $lesseq($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(175,plain,
% 0.19/0.52 ($lesseq($sum(I!4, $product(-1, tb2t2(t2tb2(I!4)))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[174, 166])).
% 0.19/0.52 tff(176,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[175, 173, 172])).
% 0.19/0.52 tff(177,plain,($lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(178,plain,
% 0.19/0.52 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : refl(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(179,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.52 tff(180,plain,
% 0.19/0.52 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))) <=> (~((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) <=> (~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))))), rewrite((~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(181,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.52 tff(182,plain,
% 0.19/0.52 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(rewrite((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))), trans(monotonicity(rewrite($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = $sum($product(-1, nb_occ(A, I, J, C)), nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))), (($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) <=> ($sum($product(-1, nb_occ(A, I, J, C)), nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C)) = 0))), rewrite(($sum($product(-1, nb_occ(A, I, J, C)), nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C)) = 0) <=> ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)), (($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) <=> ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(183,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[182])).
% 0.19/0.52 tff(184,plain,
% 0.19/0.52 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(rewrite((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) <=> ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)), rewrite((~($lesseq(I, K) & (~$lesseq(J, K)))) <=> (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(185,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.52 tff(186,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(187,plain,
% 0.19/0.52 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(rewrite(($lesseq(I, K) & $less(K, J)) <=> ($lesseq(I, K) & (~$lesseq(J, K)))), trans(monotonicity(rewrite(((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))), (((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))) <=> ((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))))), rewrite(((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))), (((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C))))), ((($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C))))) <=> (($lesseq(I, K) & (~$lesseq(J, K))) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))))), rewrite((($lesseq(I, K) & (~$lesseq(J, K))) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))), ((($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(188,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : (($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.52 tff(189,axiom,(![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : (($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nb_occ_store_neq_neq')).
% 0.19/0.52 tff(190,plain,
% 0.19/0.52 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.44/0.53 tff(191,plain,
% 0.44/0.53 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = nb_occ(A, I, J, C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.44/0.53 tff(192,plain,
% 0.44/0.53 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[191, 185])).
% 0.44/0.53 tff(193,plain,
% 0.44/0.53 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0))),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[192, 183])).
% 0.44/0.53 tff(194,plain,(
% 0.44/0.53 ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0))),
% 0.44/0.53 inference(skolemize,[status(sab)],[193])).
% 0.44/0.53 tff(195,plain,
% 0.44/0.53 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[194, 181])).
% 0.44/0.53 tff(196,plain,
% 0.44/0.53 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[195, 179])).
% 0.44/0.53 tff(197,plain,
% 0.44/0.53 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0))),
% 0.44/0.53 inference(rewrite,[status(thm)],[])).
% 0.44/0.53 tff(198,plain,
% 0.44/0.53 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0))) <=> ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0))),
% 0.44/0.53 inference(rewrite,[status(thm)],[])).
% 0.44/0.53 tff(199,plain,
% 0.44/0.53 ((~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) <=> (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0))),
% 0.44/0.53 inference(rewrite,[status(thm)],[])).
% 0.44/0.53 tff(200,plain,
% 0.44/0.53 ($greatereq($sum($product(-1, K2!8), tb2t2(t2tb2(I!4))), 0) <=> $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0)),
% 0.44/0.53 inference(rewrite,[status(thm)],[])).
% 0.44/0.53 tff(201,plain,
% 0.44/0.53 ($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)) = $sum($product(-1, K2!8), tb2t2(t2tb2(I!4)))),
% 0.44/0.53 inference(rewrite,[status(thm)],[])).
% 0.44/0.53 tff(202,plain,
% 0.44/0.53 ($greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) <=> $greatereq($sum($product(-1, K2!8), tb2t2(t2tb2(I!4))), 0)),
% 0.44/0.53 inference(monotonicity,[status(thm)],[201])).
% 0.44/0.53 tff(203,plain,
% 0.44/0.53 ($greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) <=> $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0)),
% 0.44/0.53 inference(transitivity,[status(thm)],[202, 200])).
% 0.44/0.53 tff(204,plain,
% 0.44/0.53 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0))) <=> ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)))),
% 0.44/0.53 inference(monotonicity,[status(thm)],[203, 199])).
% 0.44/0.53 tff(205,plain,
% 0.44/0.53 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0))) <=> ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0))),
% 0.44/0.53 inference(transitivity,[status(thm)],[204, 198])).
% 0.44/0.53 tff(206,plain,
% 0.44/0.53 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0)))),
% 0.44/0.53 inference(monotonicity,[status(thm)],[205])).
% 0.44/0.53 tff(207,plain,
% 0.44/0.53 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0))),
% 0.44/0.53 inference(transitivity,[status(thm)],[206, 197])).
% 0.44/0.53 tff(208,plain,
% 0.44/0.53 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)))),
% 0.44/0.53 inference(quant_inst,[status(thm)],[])).
% 0.44/0.53 tff(209,plain,
% 0.44/0.53 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0)),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.44/0.53 tff(210,plain,
% 0.44/0.53 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = C!7) | ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0)),
% 0.44/0.53 inference(unit_resolution,[status(thm)],[209, 196, 177, 171, 130])).
% 0.44/0.53 tff(211,plain,
% 0.44/0.53 ($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0),
% 0.44/0.53 inference(unit_resolution,[status(thm)],[210, 125])).
% 0.44/0.53 tff(212,plain,
% 0.44/0.53 ((~($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0)) | $lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.44/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.44/0.53 tff(213,plain,
% 0.44/0.53 ($lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.44/0.53 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.44/0.53 tff(214,plain,
% 0.44/0.53 (A2!6 = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.44/0.53 inference(and_elim,[status(thm)],[148])).
% 0.44/0.53 tff(215,plain,
% 0.44/0.53 (tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4)))) = A2!6),
% 0.44/0.53 inference(symmetry,[status(thm)],[214])).
% 0.44/0.53 tff(216,plain,
% 0.44/0.53 ((~![A: ty, B: ty, X: uni, X1: uni] : sort(B, get(B, A, X, X1))) | sort(color1, get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.44/0.53 inference(quant_inst,[status(thm)],[])).
% 0.44/0.53 tff(217,plain,
% 0.44/0.53 (sort(color1, get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.44/0.53 inference(unit_resolution,[status(thm)],[216, 7])).
% 0.44/0.53 tff(218,plain,
% 0.44/0.53 (((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(I!4))))) <=> ((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.44/0.53 inference(rewrite,[status(thm)],[])).
% 0.44/0.53 tff(219,plain,
% 0.44/0.53 ((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | ((~sort(color1, get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.44/0.53 inference(quant_inst,[status(thm)],[])).
% 0.44/0.53 tff(220,plain,
% 0.44/0.53 ((~![J: uni] : ((~sort(color1, J)) | (t2tb1(tb2t1(J)) = J))) | (~sort(color1, get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.44/0.53 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.44/0.53 tff(221,plain,
% 0.44/0.53 (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(I!4))),
% 0.44/0.53 inference(unit_resolution,[status(thm)],[220, 19, 217])).
% 0.44/0.53 tff(222,plain,
% 0.44/0.53 (A1!2 = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.44/0.54 inference(and_elim,[status(thm)],[148])).
% 0.44/0.54 tff(223,plain,
% 0.44/0.54 (t2tb(A1!2) = t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.44/0.54 inference(monotonicity,[status(thm)],[222])).
% 0.44/0.54 tff(224,plain,
% 0.44/0.54 (t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))) = t2tb(A1!2)),
% 0.44/0.54 inference(symmetry,[status(thm)],[223])).
% 0.44/0.54 tff(225,plain,
% 0.44/0.54 (set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) = set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.44/0.54 inference(monotonicity,[status(thm)],[224, 87, 221])).
% 0.44/0.54 tff(226,plain,
% 0.44/0.54 (tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.44/0.54 inference(monotonicity,[status(thm)],[225])).
% 0.44/0.54 tff(227,plain,
% 0.44/0.54 (tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = A2!6),
% 0.44/0.54 inference(transitivity,[status(thm)],[226, 215])).
% 0.44/0.54 tff(228,plain,
% 0.44/0.54 (nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7) = nb_occ(A2!6, K1!9, K2!8, C!7)),
% 0.44/0.54 inference(monotonicity,[status(thm)],[227])).
% 0.44/0.54 tff(229,plain,
% 0.44/0.54 (nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7)),
% 0.44/0.54 inference(symmetry,[status(thm)],[228])).
% 0.44/0.54 tff(230,plain,
% 0.44/0.54 ((~(nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) | $greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.44/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.44/0.54 tff(231,plain,
% 0.44/0.54 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.44/0.54 tff(232,plain,
% 0.44/0.54 ($greatereq($sum(J!3, $product(-1, K1!9)), 0)),
% 0.44/0.54 inference(and_elim,[status(thm)],[150])).
% 0.44/0.54 tff(233,assumption,(~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)), introduced(assumption)).
% 0.44/0.54 tff(234,plain,
% 0.44/0.54 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))) = 0)),
% 0.44/0.54 inference(quant_inst,[status(thm)],[])).
% 0.44/0.54 tff(235,plain,
% 0.44/0.54 ($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))) = 0),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[234, 164])).
% 0.44/0.54 tff(236,plain,
% 0.44/0.54 ((~($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))) = 0)) | $lesseq($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))), 0)),
% 0.44/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.44/0.54 tff(237,plain,
% 0.44/0.54 ($lesseq($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))), 0)),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.44/0.54 tff(238,plain,
% 0.44/0.54 ($false),
% 0.44/0.54 inference(theory_lemma,[status(thm)],[237, 233, 232])).
% 0.44/0.54 tff(239,plain,($lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.54 tff(240,plain,
% 0.44/0.54 (~$greatereq($sum(J!3, $product(-1, K2!8)), 0)),
% 0.44/0.54 inference(and_elim,[status(thm)],[150])).
% 0.44/0.54 tff(241,assumption,($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0)), introduced(assumption)).
% 0.44/0.54 tff(242,plain,
% 0.44/0.54 ((~($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))) = 0)) | $greatereq($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))), 0)),
% 0.44/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.44/0.54 tff(243,plain,
% 0.44/0.54 ($greatereq($sum(J!3, $product(-1, tb2t2(t2tb2(J!3)))), 0)),
% 0.44/0.54 inference(unit_resolution,[status(thm)],[242, 235])).
% 0.44/0.54 tff(244,plain,
% 0.44/0.54 ($false),
% 0.44/0.54 inference(theory_lemma,[status(thm)],[243, 241, 240])).
% 0.44/0.54 tff(245,plain,(~$lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.54 tff(246,plain,
% 0.44/0.54 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0))),
% 0.44/0.54 inference(rewrite,[status(thm)],[])).
% 0.44/0.54 tff(247,plain,
% 0.44/0.54 (((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0))) <=> ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(248,plain,
% 0.46/0.54 ((~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) <=> (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(249,plain,
% 0.46/0.54 ($greatereq($sum($product(-1, K2!8), tb2t2(t2tb2(J!3))), 0) <=> $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0)),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(250,plain,
% 0.46/0.54 ($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)) = $sum($product(-1, K2!8), tb2t2(t2tb2(J!3)))),
% 0.46/0.54 inference(rewrite,[status(thm)],[])).
% 0.46/0.54 tff(251,plain,
% 0.46/0.54 ($greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) <=> $greatereq($sum($product(-1, K2!8), tb2t2(t2tb2(J!3))), 0)),
% 0.46/0.54 inference(monotonicity,[status(thm)],[250])).
% 0.46/0.54 tff(252,plain,
% 0.46/0.54 ($greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) <=> $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0)),
% 0.46/0.54 inference(transitivity,[status(thm)],[251, 249])).
% 0.46/0.54 tff(253,plain,
% 0.46/0.54 (((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0))) <=> ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))),
% 0.46/0.54 inference(monotonicity,[status(thm)],[252, 248])).
% 0.46/0.54 tff(254,plain,
% 0.46/0.54 (((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0))) <=> ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0))),
% 0.46/0.54 inference(transitivity,[status(thm)],[253, 247])).
% 0.46/0.54 tff(255,plain,
% 0.46/0.54 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0)))),
% 0.46/0.54 inference(monotonicity,[status(thm)],[254])).
% 0.46/0.54 tff(256,plain,
% 0.46/0.54 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0))),
% 0.46/0.55 inference(transitivity,[status(thm)],[255, 246])).
% 0.46/0.55 tff(257,plain,
% 0.46/0.55 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)))),
% 0.46/0.55 inference(quant_inst,[status(thm)],[])).
% 0.46/0.55 tff(258,plain,
% 0.46/0.55 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (C = Cqt) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 0) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0)),
% 0.46/0.55 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.46/0.55 tff(259,plain,
% 0.46/0.55 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[258, 196])).
% 0.46/0.55 tff(260,plain,
% 0.46/0.55 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[259, 245, 239])).
% 0.46/0.55 tff(261,plain,
% 0.46/0.55 ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[260, 124, 114])).
% 0.46/0.55 tff(262,plain,
% 0.46/0.55 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0)) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(263,plain,
% 0.46/0.55 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.46/0.55 tff(264,plain,
% 0.46/0.55 (set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[117, 23])).
% 0.46/0.55 tff(265,plain,
% 0.46/0.55 (tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.55 inference(monotonicity,[status(thm)],[264])).
% 0.46/0.55 tff(266,plain,
% 0.46/0.55 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7)),
% 0.46/0.55 inference(monotonicity,[status(thm)],[265])).
% 0.46/0.55 tff(267,plain,
% 0.46/0.55 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7)),
% 0.46/0.55 inference(symmetry,[status(thm)],[266])).
% 0.46/0.55 tff(268,plain,
% 0.46/0.55 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(269,plain,
% 0.46/0.55 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.46/0.55 tff(270,plain,
% 0.46/0.55 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 0)) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(271,plain,
% 0.46/0.55 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[270, 261])).
% 0.46/0.55 tff(272,plain,
% 0.46/0.55 ((~($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) = 0)) | $greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(273,plain,
% 0.46/0.55 ($greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[272, 211])).
% 0.46/0.55 tff(274,plain,
% 0.46/0.55 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(275,plain,
% 0.46/0.55 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[274, 267])).
% 0.46/0.55 tff(276,plain,
% 0.46/0.55 ((~(nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) | $lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.55 tff(277,plain,
% 0.46/0.55 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)),
% 0.46/0.55 inference(unit_resolution,[status(thm)],[276, 229])).
% 0.46/0.55 tff(278,plain,
% 0.46/0.55 ((~$greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)) | (~$lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)) | $lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.46/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.56 tff(279,plain,
% 0.46/0.56 ((~$greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, C!7))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)) | $lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[278, 277, 275])).
% 0.46/0.56 tff(280,plain,
% 0.46/0.56 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[279, 273, 271])).
% 0.46/0.56 tff(281,plain,
% 0.46/0.56 (~($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0)),
% 0.46/0.56 inference(or_elim,[status(thm)],[149])).
% 0.46/0.56 tff(282,plain,
% 0.46/0.56 (($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0) | (~$lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)) | (~$greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0))),
% 0.46/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.56 tff(283,plain,
% 0.46/0.56 ((~$lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)) | (~$greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0))),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.46/0.56 tff(284,plain,
% 0.46/0.56 (~$greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[283, 280])).
% 0.46/0.56 tff(285,plain,
% 0.46/0.56 ($false),
% 0.46/0.56 inference(theory_lemma,[status(thm)],[284, 269, 263, 231, 213])).
% 0.46/0.56 tff(286,plain,((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.56 tff(287,plain,
% 0.46/0.56 (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[286, 114])).
% 0.46/0.56 tff(288,plain,
% 0.46/0.56 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = C!7),
% 0.46/0.56 inference(symmetry,[status(thm)],[287])).
% 0.46/0.56 tff(289,plain,
% 0.46/0.56 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7)),
% 0.46/0.56 inference(monotonicity,[status(thm)],[265, 288])).
% 0.46/0.56 tff(290,plain,
% 0.46/0.56 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.56 inference(symmetry,[status(thm)],[289])).
% 0.46/0.56 tff(291,plain,
% 0.46/0.56 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.56 tff(292,plain,
% 0.46/0.56 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.46/0.56 tff(293,plain,
% 0.46/0.56 (nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = nb_occ(A!5, K1!9, K2!8, C!7)),
% 0.46/0.56 inference(monotonicity,[status(thm)],[288])).
% 0.46/0.56 tff(294,plain,
% 0.46/0.56 (nb_occ(A!5, K1!9, K2!8, C!7) = nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.56 inference(symmetry,[status(thm)],[293])).
% 0.46/0.56 tff(295,plain,
% 0.46/0.56 ((~(nb_occ(A!5, K1!9, K2!8, C!7) = nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.56 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.56 tff(296,plain,
% 0.46/0.56 ($lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.56 inference(unit_resolution,[status(thm)],[295, 294])).
% 0.46/0.56 tff(297,plain,
% 0.46/0.56 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[288])).
% 0.46/0.56 tff(298,plain,
% 0.46/0.56 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.56 inference(symmetry,[status(thm)],[297])).
% 0.46/0.56 tff(299,plain,
% 0.46/0.56 ((~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) <=> (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.46/0.56 inference(monotonicity,[status(thm)],[298])).
% 0.46/0.56 tff(300,plain,
% 0.46/0.56 (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[130, 299])).
% 0.46/0.56 tff(301,plain,
% 0.46/0.56 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : refl(((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0))))),
% 0.46/0.56 inference(bind,[status(th)],[])).
% 0.46/0.56 tff(302,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.46/0.56 inference(quant_intro,[status(thm)],[301])).
% 0.46/0.56 tff(303,plain,
% 0.46/0.56 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))) <=> (~((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) <=> (~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))))), rewrite((~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0)))), (((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0))))), rewrite(((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $greatereq($sum(K, $product(-1, J)), 0))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))), (((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))))),
% 0.46/0.56 inference(bind,[status(th)],[])).
% 0.46/0.56 tff(304,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.46/0.56 inference(quant_intro,[status(thm)],[303])).
% 0.46/0.56 tff(305,plain,
% 0.46/0.56 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(trans(monotonicity(rewrite($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = $sum($product(-1, nb_occ(A, I, J, C)), nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))), (($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) <=> ($sum($product(-1, nb_occ(A, I, J, C)), nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C)) = -1))), rewrite(($sum($product(-1, nb_occ(A, I, J, C)), nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C)) = -1) <=> ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1)), (($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) <=> ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1))), rewrite((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))), (((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))))), rewrite(((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))))), (((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))))))),
% 0.46/0.56 inference(bind,[status(th)],[])).
% 0.46/0.56 tff(306,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))))),
% 0.46/0.56 inference(quant_intro,[status(thm)],[305])).
% 0.46/0.56 tff(307,plain,
% 0.46/0.56 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(rewrite((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) <=> ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1)), rewrite((~($lesseq(I, K) & (~$lesseq(J, K)))) <=> (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))), (((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))))), rewrite(((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))), (((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))))),
% 0.46/0.56 inference(bind,[status(th)],[])).
% 0.46/0.56 tff(308,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))),
% 0.46/0.56 inference(quant_intro,[status(thm)],[307])).
% 0.46/0.56 tff(309,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.56 inference(rewrite,[status(thm)],[])).
% 0.46/0.56 tff(310,plain,
% 0.46/0.56 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : trans(monotonicity(rewrite(($lesseq(I, K) & $less(K, J)) <=> ($lesseq(I, K) & (~$lesseq(J, K)))), trans(monotonicity(trans(monotonicity(rewrite((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1)) <=> (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C)))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C)))))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C)))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C)))))), (((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1)))) <=> ((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))))))), rewrite(((~(C = Cqt)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))))), (((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1)))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C)))))), ((($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1))))) <=> (($lesseq(I, K) & (~$lesseq(J, K))) => ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))))))), rewrite((($lesseq(I, K) & (~$lesseq(J, K))) => ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))), ((($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1))))) <=> ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))))),
% 0.46/0.56 inference(bind,[status(th)],[])).
% 0.46/0.56 tff(311,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : (($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.56 inference(quant_intro,[status(thm)],[310])).
% 0.46/0.56 tff(312,axiom,(![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : (($lesseq(I, K) & $less(K, J)) => ((~(C = Cqt)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $difference(nb_occ(A, I, J, C), 1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nb_occ_store_neq_eq')).
% 0.46/0.56 tff(313,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.46/0.56 tff(314,plain,
% 0.46/0.56 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C) = $sum(-1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.56 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.46/0.56 tff(315,plain,
% 0.46/0.57 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = -1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[314, 308])).
% 0.46/0.57 tff(316,plain,
% 0.46/0.57 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[315, 306])).
% 0.46/0.57 tff(317,plain,(
% 0.46/0.57 ![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$greatereq($sum(K, $product(-1, J)), 0)))))),
% 0.46/0.57 inference(skolemize,[status(sab)],[316])).
% 0.46/0.57 tff(318,plain,
% 0.46/0.57 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[317, 304])).
% 0.46/0.57 tff(319,plain,
% 0.46/0.57 (![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[318, 302])).
% 0.46/0.57 tff(320,plain,
% 0.46/0.57 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(321,plain,
% 0.46/0.57 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0))) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(322,plain,
% 0.46/0.57 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0))) <=> ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[203, 199])).
% 0.46/0.57 tff(323,plain,
% 0.46/0.57 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0))) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))))),
% 0.46/0.57 inference(transitivity,[status(thm)],[322, 321])).
% 0.46/0.57 tff(324,plain,
% 0.46/0.57 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[323])).
% 0.46/0.57 tff(325,plain,
% 0.46/0.57 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))))),
% 0.46/0.57 inference(transitivity,[status(thm)],[324, 320])).
% 0.46/0.57 tff(326,plain,
% 0.46/0.57 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) | $greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K2!8)), 0) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(327,plain,
% 0.46/0.57 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.46/0.57 tff(328,plain,
% 0.46/0.57 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[327, 319, 177, 171])).
% 0.46/0.57 tff(329,plain,
% 0.46/0.57 ($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[328, 300, 119])).
% 0.46/0.57 tff(330,plain,
% 0.46/0.57 ((~($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1)) | $lesseq($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 1)),
% 0.46/0.57 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.57 tff(331,plain,
% 0.46/0.57 ($lesseq($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 1)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[330, 329])).
% 0.46/0.57 tff(332,plain,
% 0.46/0.57 (nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = nb_occ(A2!6, K1!9, K2!8, C!7)),
% 0.46/0.58 inference(monotonicity,[status(thm)],[227, 288])).
% 0.46/0.58 tff(333,plain,
% 0.46/0.58 (nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.58 inference(symmetry,[status(thm)],[332])).
% 0.46/0.58 tff(334,plain,
% 0.46/0.58 ((~(nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.58 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.58 tff(335,plain,
% 0.46/0.58 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[334, 333])).
% 0.46/0.58 tff(336,plain,
% 0.46/0.58 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7)),
% 0.46/0.58 inference(monotonicity,[status(thm)],[288])).
% 0.46/0.58 tff(337,plain,
% 0.46/0.58 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.58 inference(symmetry,[status(thm)],[336])).
% 0.46/0.58 tff(338,plain,
% 0.46/0.58 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.58 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.58 tff(339,plain,
% 0.46/0.58 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.58 inference(unit_resolution,[status(thm)],[338, 337])).
% 0.46/0.58 tff(340,plain,
% 0.46/0.58 ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))) = C!7)),
% 0.46/0.58 inference(monotonicity,[status(thm)],[113, 288])).
% 0.46/0.58 tff(341,plain,
% 0.46/0.58 ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.58 inference(transitivity,[status(thm)],[340, 126])).
% 0.46/0.58 tff(342,plain,
% 0.46/0.58 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) <=> (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.58 inference(symmetry,[status(thm)],[341])).
% 0.46/0.58 tff(343,plain,
% 0.46/0.58 ((~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) <=> (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[342])).
% 0.46/0.58 tff(344,plain,
% 0.46/0.58 (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[130, 343])).
% 0.46/0.58 tff(345,plain,
% 0.46/0.58 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : refl(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(346,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[345])).
% 0.46/0.58 tff(347,plain,
% 0.46/0.58 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))) <=> (~((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> (~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))))), rewrite((~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(348,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[347])).
% 0.46/0.58 tff(349,plain,
% 0.46/0.58 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(rewrite((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(350,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[349])).
% 0.46/0.58 tff(351,plain,
% 0.46/0.58 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(rewrite((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) <=> ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1)), rewrite((~($lesseq(I, K) & (~$lesseq(J, K)))) <=> (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))), (((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(352,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[351])).
% 0.46/0.58 tff(353,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(354,plain,
% 0.46/0.58 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(rewrite(($lesseq(I, K) & $less(K, J)) <=> ($lesseq(I, K) & (~$lesseq(J, K)))), trans(monotonicity(rewrite((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1)) <=> (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C)))), (((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C)))))), rewrite(((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C)))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))))), (((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C)))))), ((($lesseq(I, K) & $less(K, J)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1)))) <=> (($lesseq(I, K) & (~$lesseq(J, K))) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))))))), rewrite((($lesseq(I, K) & (~$lesseq(J, K))) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))), ((($lesseq(I, K) & $less(K, J)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1)))) <=> ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(355,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : (($lesseq(I, K) & $less(K, J)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1)))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[354])).
% 0.46/0.58 tff(356,axiom,(![A: map_int_color, I: $int, J: $int, K: $int, C: color] : (($lesseq(I, K) & $less(K, J)) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(nb_occ(A, I, J, C), 1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nb_occ_store_eq_neq')).
% 0.46/0.58 tff(357,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.46/0.58 tff(358,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = $sum(1, nb_occ(A, I, J, C))) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[357, 353])).
% 0.46/0.58 tff(359,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[358, 352])).
% 0.46/0.58 tff(360,plain,
% 0.46/0.58 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[359, 350])).
% 0.46/0.58 tff(361,plain,(
% 0.46/0.58 ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.58 inference(skolemize,[status(sab)],[360])).
% 0.46/0.59 tff(362,plain,
% 0.46/0.59 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[361, 348])).
% 0.46/0.59 tff(363,plain,
% 0.46/0.59 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))),
% 0.46/0.59 inference(modus_ponens,[status(thm)],[362, 346])).
% 0.46/0.59 tff(364,plain,
% 0.46/0.59 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(365,plain,
% 0.46/0.59 (((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(366,plain,
% 0.46/0.59 (($sum($product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))), nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) = 1) <=> ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1)),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(367,plain,
% 0.46/0.59 ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = $sum($product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))), nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.59 inference(rewrite,[status(thm)],[])).
% 0.46/0.59 tff(368,plain,
% 0.46/0.59 (($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) <=> ($sum($product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))), nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) = 1)),
% 0.46/0.59 inference(monotonicity,[status(thm)],[367])).
% 0.46/0.59 tff(369,plain,
% 0.46/0.59 (($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1) <=> ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1)),
% 0.46/0.59 inference(transitivity,[status(thm)],[368, 366])).
% 0.46/0.59 tff(370,plain,
% 0.46/0.59 (((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1)) <=> ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[248, 369])).
% 0.46/0.59 tff(371,plain,
% 0.46/0.59 (((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[370, 365])).
% 0.46/0.59 tff(372,plain,
% 0.46/0.59 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))))),
% 0.46/0.59 inference(monotonicity,[status(thm)],[371])).
% 0.46/0.59 tff(373,plain,
% 0.46/0.59 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))),
% 0.46/0.59 inference(transitivity,[status(thm)],[372, 364])).
% 0.46/0.59 tff(374,plain,
% 0.46/0.59 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ((tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(375,plain,
% 0.46/0.60 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.46/0.60 tff(376,plain,
% 0.46/0.60 (($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1) | (tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[375, 363, 245, 239])).
% 0.46/0.60 tff(377,plain,
% 0.46/0.60 ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[376, 344])).
% 0.46/0.60 tff(378,plain,
% 0.46/0.60 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1)) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), -1)),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(379,plain,
% 0.46/0.60 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), -1)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[378, 377])).
% 0.46/0.60 tff(380,plain,
% 0.46/0.60 ((~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), -1))),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(381,plain,
% 0.46/0.60 (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[380, 379])).
% 0.46/0.60 tff(382,plain,
% 0.46/0.60 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0) | (~$lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0) | (~$greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$lesseq($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 1))),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(383,plain,
% 0.46/0.60 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[382, 381, 339, 335, 331, 296, 292])).
% 0.46/0.60 tff(384,plain,
% 0.46/0.60 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(385,plain,
% 0.46/0.60 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[384, 290])).
% 0.46/0.60 tff(386,plain,
% 0.46/0.60 ((~(nb_occ(A!5, K1!9, K2!8, C!7) = nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(387,plain,
% 0.46/0.60 ($greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[386, 294])).
% 0.46/0.60 tff(388,plain,
% 0.46/0.60 ((~($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = 1)) | $greatereq($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 1)),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(389,plain,
% 0.46/0.60 ($greatereq($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 1)),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[388, 329])).
% 0.46/0.60 tff(390,plain,
% 0.46/0.60 ((~(nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.60 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.60 tff(391,plain,
% 0.46/0.60 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[390, 333])).
% 0.46/0.61 tff(392,plain,
% 0.46/0.61 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.61 tff(393,plain,
% 0.46/0.61 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[392, 337])).
% 0.46/0.61 tff(394,plain,
% 0.46/0.61 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))) = -1)) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), -1)),
% 0.46/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.61 tff(395,plain,
% 0.46/0.61 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), -1)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[394, 377])).
% 0.46/0.61 tff(396,plain,
% 0.46/0.61 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0) | (~$greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), -1)) | (~$lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 0)) | (~$greatereq($sum(nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), 1))),
% 0.46/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.61 tff(397,plain,
% 0.46/0.61 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[396, 395, 393, 391, 389, 387, 385])).
% 0.46/0.61 tff(398,plain,
% 0.46/0.61 ($false),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[283, 397, 383])).
% 0.46/0.61 tff(399,plain,(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7), inference(lemma,lemma(discharge,[]))).
% 0.46/0.61 tff(400,plain,
% 0.46/0.61 (C!7 = tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3)))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[399])).
% 0.46/0.61 tff(401,plain,
% 0.46/0.61 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))) = tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3)))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[113])).
% 0.46/0.61 tff(402,plain,
% 0.46/0.61 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))) = C!7),
% 0.46/0.61 inference(transitivity,[status(thm)],[401, 399])).
% 0.46/0.61 tff(403,plain,
% 0.46/0.61 (nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = nb_occ(A!5, K1!9, K2!8, C!7)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[402])).
% 0.46/0.61 tff(404,plain,
% 0.46/0.61 (nb_occ(A!5, K1!9, K2!8, C!7) = nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[403])).
% 0.46/0.61 tff(405,plain,
% 0.46/0.61 ((~(nb_occ(A!5, K1!9, K2!8, C!7) = nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.46/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.61 tff(406,plain,
% 0.46/0.61 ($lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[405, 404])).
% 0.46/0.61 tff(407,plain,
% 0.46/0.61 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[265, 402])).
% 0.46/0.61 tff(408,plain,
% 0.46/0.61 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[407])).
% 0.46/0.61 tff(409,plain,
% 0.46/0.61 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.46/0.61 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.61 tff(410,plain,
% 0.46/0.61 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[409, 408])).
% 0.46/0.61 tff(411,plain,
% 0.46/0.61 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = C!7)),
% 0.46/0.61 inference(monotonicity,[status(thm)],[119, 402])).
% 0.46/0.61 tff(412,plain,
% 0.46/0.61 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) <=> (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[411, 115])).
% 0.46/0.61 tff(413,plain,
% 0.46/0.61 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) <=> (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.61 inference(symmetry,[status(thm)],[412])).
% 0.46/0.61 tff(414,plain,
% 0.46/0.61 ((~(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))) <=> (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[413])).
% 0.46/0.61 tff(415,plain,
% 0.46/0.61 (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[124, 414])).
% 0.46/0.61 tff(416,plain,
% 0.46/0.61 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(417,plain,
% 0.46/0.61 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(418,plain,
% 0.46/0.62 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)) <=> ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[199])).
% 0.46/0.62 tff(419,plain,
% 0.46/0.62 (((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))),
% 0.46/0.62 inference(transitivity,[status(thm)],[418, 417])).
% 0.46/0.62 tff(420,plain,
% 0.46/0.62 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[419])).
% 0.46/0.62 tff(421,plain,
% 0.46/0.62 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))),
% 0.46/0.62 inference(transitivity,[status(thm)],[420, 416])).
% 0.46/0.62 tff(422,plain,
% 0.46/0.62 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1))),
% 0.46/0.62 inference(quant_inst,[status(thm)],[])).
% 0.46/0.62 tff(423,plain,
% 0.46/0.62 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 1))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)),
% 0.46/0.62 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.46/0.62 tff(424,plain,
% 0.46/0.62 ((tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[423, 363, 177, 171])).
% 0.46/0.62 tff(425,plain,
% 0.46/0.62 ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[424, 415])).
% 0.46/0.62 tff(426,plain,
% 0.46/0.62 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 1)),
% 0.46/0.62 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.62 tff(427,plain,
% 0.46/0.62 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 1)),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[426, 425])).
% 0.46/0.62 tff(428,plain,
% 0.46/0.62 ((~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 1))),
% 0.46/0.62 inference(theory_lemma,[status(thm)],[])).
% 0.46/0.62 tff(429,plain,
% 0.46/0.62 (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[428, 427])).
% 0.46/0.62 tff(430,plain,
% 0.46/0.62 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(431,plain,
% 0.46/0.62 (((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0))) <=> ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))),
% 0.46/0.62 inference(rewrite,[status(thm)],[])).
% 0.46/0.62 tff(432,plain,
% 0.46/0.62 (((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0))) <=> ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))),
% 0.46/0.62 inference(monotonicity,[status(thm)],[252, 248])).
% 0.46/0.62 tff(433,plain,
% 0.46/0.62 (((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0))) <=> ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))),
% 0.46/0.63 inference(transitivity,[status(thm)],[432, 431])).
% 0.46/0.63 tff(434,plain,
% 0.46/0.63 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[433])).
% 0.46/0.63 tff(435,plain,
% 0.46/0.63 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)))),
% 0.55/0.63 inference(transitivity,[status(thm)],[434, 430])).
% 0.55/0.63 tff(436,plain,
% 0.55/0.63 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | $greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K2!8)), 0) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)))),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(437,plain,
% 0.55/0.63 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color, Cqt: color] : ((C = Cqt) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $greatereq($sum(K, $product(-1, J)), 0) | ($sum(nb_occ(A, I, J, C), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(Cqt))), I, J, C))) = 1) | (~$greatereq($sum(K, $product(-1, I)), 0)))) | (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.55/0.63 tff(438,plain,
% 0.55/0.63 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[437, 319])).
% 0.55/0.63 tff(439,plain,
% 0.55/0.63 ((C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = C!7)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[438, 245, 239])).
% 0.55/0.63 tff(440,plain,
% 0.55/0.63 ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[439, 124, 399])).
% 0.55/0.63 tff(441,plain,
% 0.55/0.63 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1)) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 1)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.63 tff(442,plain,
% 0.55/0.63 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 1)),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[441, 440])).
% 0.55/0.63 tff(443,plain,
% 0.55/0.63 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0) | (~$lesseq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 1)) | (~$greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.63 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.64 tff(444,plain,
% 0.55/0.64 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[443, 442, 231, 429, 410, 406])).
% 0.55/0.64 tff(445,plain,
% 0.55/0.64 ((~(nb_occ(A!5, K1!9, K2!8, C!7) = nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.64 tff(446,plain,
% 0.55/0.64 ($greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[445, 404])).
% 0.55/0.64 tff(447,plain,
% 0.55/0.64 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.64 tff(448,plain,
% 0.55/0.64 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[447, 408])).
% 0.55/0.64 tff(449,plain,
% 0.55/0.64 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 1)) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 1)),
% 0.55/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.64 tff(450,plain,
% 0.55/0.64 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 1)),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[449, 425])).
% 0.55/0.64 tff(451,plain,
% 0.55/0.64 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))) = 1)) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 1)),
% 0.55/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.64 tff(452,plain,
% 0.55/0.64 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 1)),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[451, 440])).
% 0.55/0.64 tff(453,plain,
% 0.55/0.64 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0) | (~$greatereq($sum(nb_occ(A!5, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)) | (~$greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 1)) | (~$lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))))), K1!9, K2!8, C!7))), 0)) | (~$lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 1))),
% 0.55/0.64 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.64 tff(454,plain,
% 0.55/0.64 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))), 0)),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[453, 452, 277, 450, 448, 446])).
% 0.55/0.64 tff(455,plain,
% 0.55/0.64 ($false),
% 0.55/0.64 inference(unit_resolution,[status(thm)],[283, 454, 444])).
% 0.55/0.64 tff(456,plain,(C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.64 tff(457,plain,
% 0.55/0.64 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = C!7),
% 0.55/0.64 inference(symmetry,[status(thm)],[456])).
% 0.55/0.64 tff(458,plain,
% 0.55/0.64 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.55/0.64 inference(transitivity,[status(thm)],[457, 400, 113])).
% 0.55/0.64 tff(459,plain,
% 0.55/0.64 (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4)))) = t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.55/0.64 inference(monotonicity,[status(thm)],[458])).
% 0.55/0.64 tff(460,plain,
% 0.55/0.64 (get(color1, int, t2tb(A!5), t2tb2(I!4)) = t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.55/0.64 inference(symmetry,[status(thm)],[221])).
% 0.55/0.64 tff(461,plain,
% 0.55/0.64 (get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4)))) = get(color1, int, t2tb(A!5), t2tb2(J!3))),
% 0.55/0.64 inference(transitivity,[status(thm)],[118, 460, 459, 23])).
% 0.55/0.64 tff(462,plain,
% 0.55/0.64 (tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.55/0.64 inference(monotonicity,[status(thm)],[461])).
% 0.55/0.64 tff(463,plain,
% 0.55/0.64 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : refl(((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(464,plain,
% 0.55/0.64 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[463])).
% 0.55/0.64 tff(465,plain,
% 0.55/0.64 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))) <=> (~((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> (~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))))), rewrite((~(~((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0))), ((~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)))), (((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)))), rewrite(((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ((~$greatereq($sum(K, $product(-1, I)), 0)) | $lesseq($sum(J, $product(-1, K)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))), (((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(466,plain,
% 0.55/0.64 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[465])).
% 0.55/0.64 tff(467,plain,
% 0.55/0.64 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(rewrite((~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) <=> (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))), (((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))))), rewrite(((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))), (((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(468,plain,
% 0.55/0.64 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.64 inference(quant_intro,[status(thm)],[467])).
% 0.55/0.64 tff(469,plain,
% 0.55/0.64 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(rewrite((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) <=> ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0)), rewrite((~($lesseq(I, K) & (~$lesseq(J, K)))) <=> (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))), (((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> (($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))))), rewrite((($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0))))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))), (((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))))),
% 0.55/0.64 inference(bind,[status(th)],[])).
% 0.55/0.64 tff(470,plain,
% 0.55/0.64 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[469])).
% 0.55/0.65 tff(471,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K))))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(472,plain,
% 0.55/0.65 (^[A: map_int_color, I: $int, J: $int, K: $int, C: color] : trans(monotonicity(rewrite(($lesseq(I, K) & $less(K, J)) <=> ($lesseq(I, K) & (~$lesseq(J, K)))), rewrite(((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C))) <=> ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)))), ((($lesseq(I, K) & $less(K, J)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)))) <=> (($lesseq(I, K) & (~$lesseq(J, K))) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)))))), rewrite((($lesseq(I, K) & (~$lesseq(J, K))) => ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)))) <=> ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))), ((($lesseq(I, K) & $less(K, J)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)))) <=> ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))))),
% 0.55/0.65 inference(bind,[status(th)],[])).
% 0.55/0.65 tff(473,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : (($lesseq(I, K) & $less(K, J)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)))) <=> ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.55/0.65 inference(quant_intro,[status(thm)],[472])).
% 0.55/0.65 tff(474,axiom,(![A: map_int_color, I: $int, J: $int, K: $int, C: color] : (($lesseq(I, K) & $less(K, J)) => ((tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C) => (nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nb_occ_store_eq_eq')).
% 0.55/0.65 tff(475,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.55/0.65 tff(476,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C) = nb_occ(A, I, J, C)) | (~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($lesseq(I, K) & (~$lesseq(J, K)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[475, 471])).
% 0.55/0.65 tff(477,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0) | (~($lesseq($sum(I, $product(-1, K)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[476, 470])).
% 0.55/0.65 tff(478,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[477, 468])).
% 0.55/0.65 tff(479,plain,(
% 0.55/0.65 ![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | (~($greatereq($sum(K, $product(-1, I)), 0) & (~$lesseq($sum(J, $product(-1, K)), 0)))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.65 inference(skolemize,[status(sab)],[478])).
% 0.55/0.65 tff(480,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[479, 466])).
% 0.55/0.65 tff(481,plain,
% 0.55/0.65 (![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))),
% 0.55/0.65 inference(modus_ponens,[status(thm)],[480, 464])).
% 0.55/0.65 tff(482,plain,
% 0.55/0.65 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(483,plain,
% 0.55/0.65 (((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.65 inference(rewrite,[status(thm)],[])).
% 0.55/0.65 tff(484,plain,
% 0.55/0.65 (((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) <=> ((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[199])).
% 0.55/0.65 tff(485,plain,
% 0.55/0.65 (((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.65 inference(transitivity,[status(thm)],[484, 483])).
% 0.55/0.65 tff(486,plain,
% 0.55/0.65 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)))),
% 0.55/0.65 inference(monotonicity,[status(thm)],[485])).
% 0.55/0.65 tff(487,plain,
% 0.55/0.65 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.65 inference(transitivity,[status(thm)],[486, 482])).
% 0.55/0.65 tff(488,plain,
% 0.55/0.65 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(I!4)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.65 inference(quant_inst,[status(thm)],[])).
% 0.55/0.65 tff(489,plain,
% 0.55/0.65 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(I!4)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(I!4)))), 0)) | (~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)),
% 0.55/0.66 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.55/0.66 tff(490,plain,
% 0.55/0.66 ((~(tb2t1(get(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)),
% 0.55/0.66 inference(unit_resolution,[status(thm)],[489, 481, 177, 171])).
% 0.55/0.66 tff(491,plain,
% 0.55/0.66 ($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0),
% 0.55/0.66 inference(unit_resolution,[status(thm)],[490, 462])).
% 0.55/0.66 tff(492,plain,
% 0.55/0.66 (C!7 = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))),
% 0.55/0.66 inference(transitivity,[status(thm)],[400, 113])).
% 0.55/0.66 tff(493,plain,
% 0.55/0.66 (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.55/0.66 inference(symmetry,[status(thm)],[459])).
% 0.55/0.66 tff(494,plain,
% 0.55/0.66 (t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = get(color1, int, t2tb(A!5), t2tb2(I!4))),
% 0.55/0.66 inference(transitivity,[status(thm)],[493, 221])).
% 0.55/0.66 tff(495,plain,
% 0.55/0.66 (set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) = set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4)))),
% 0.55/0.66 inference(monotonicity,[status(thm)],[224, 87, 494])).
% 0.55/0.66 tff(496,plain,
% 0.55/0.66 (tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4))))),
% 0.55/0.66 inference(monotonicity,[status(thm)],[495])).
% 0.55/0.66 tff(497,plain,
% 0.55/0.66 (tb2t(set(color1, int, t2tb(A1!2), t2tb2(J!3), get(color1, int, t2tb(A!5), t2tb2(I!4)))) = tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))))),
% 0.55/0.66 inference(symmetry,[status(thm)],[496])).
% 0.55/0.66 tff(498,plain,
% 0.55/0.66 (A2!6 = tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))))),
% 0.55/0.66 inference(transitivity,[status(thm)],[214, 497])).
% 0.55/0.66 tff(499,plain,
% 0.55/0.66 (nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.55/0.66 inference(monotonicity,[status(thm)],[498, 492])).
% 0.55/0.66 tff(500,plain,
% 0.55/0.66 ((~(nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.66 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.66 tff(501,plain,
% 0.55/0.66 ($lesseq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.66 inference(unit_resolution,[status(thm)],[500, 499])).
% 0.55/0.66 tff(502,plain,
% 0.55/0.66 ((~(nb_occ(A2!6, K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.66 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.66 tff(503,plain,
% 0.55/0.66 ($greatereq($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.66 inference(unit_resolution,[status(thm)],[502, 499])).
% 0.55/0.66 tff(504,plain,
% 0.55/0.66 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.66 inference(rewrite,[status(thm)],[])).
% 0.55/0.66 tff(505,plain,
% 0.55/0.66 (((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.66 inference(rewrite,[status(thm)],[])).
% 0.55/0.66 tff(506,plain,
% 0.55/0.66 (((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) <=> ((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.66 inference(monotonicity,[status(thm)],[248])).
% 0.55/0.66 tff(507,plain,
% 0.55/0.66 (((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) <=> ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.66 inference(transitivity,[status(thm)],[506, 505])).
% 0.55/0.66 tff(508,plain,
% 0.55/0.66 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ($lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)))),
% 0.55/0.66 inference(monotonicity,[status(thm)],[507])).
% 0.55/0.66 tff(509,plain,
% 0.55/0.66 (((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))) <=> ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.67 inference(transitivity,[status(thm)],[508, 504])).
% 0.55/0.67 tff(510,plain,
% 0.55/0.67 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | ((~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$greatereq($sum(tb2t2(t2tb2(J!3)), $product(-1, K1!9)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0))),
% 0.55/0.67 inference(quant_inst,[status(thm)],[])).
% 0.55/0.67 tff(511,plain,
% 0.55/0.67 ((~![A: map_int_color, I: $int, J: $int, K: $int, C: color] : ((~(tb2t1(get(color1, int, t2tb(A), t2tb2(K))) = C)) | $lesseq($sum(J, $product(-1, K)), 0) | (~$greatereq($sum(K, $product(-1, I)), 0)) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(A), t2tb2(K), t2tb1(C))), I, J, C), $product(-1, nb_occ(A, I, J, C))) = 0))) | $lesseq($sum(K2!8, $product(-1, tb2t2(t2tb2(J!3)))), 0) | (~$lesseq($sum(K1!9, $product(-1, tb2t2(t2tb2(J!3)))), 0)) | (~(tb2t1(get(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))))) = tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))) | ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)),
% 0.55/0.67 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.55/0.67 tff(512,plain,
% 0.55/0.67 ($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0),
% 0.55/0.67 inference(unit_resolution,[status(thm)],[511, 481, 245, 239, 113])).
% 0.55/0.67 tff(513,plain,
% 0.55/0.67 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.67 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.67 tff(514,plain,
% 0.55/0.67 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.67 inference(unit_resolution,[status(thm)],[513, 512])).
% 0.55/0.67 tff(515,plain,
% 0.55/0.67 ((~($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) = 0)) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.67 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.67 tff(516,plain,
% 0.55/0.67 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3))))), t2tb2(tb2t2(t2tb2(J!3))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.67 inference(unit_resolution,[status(thm)],[515, 512])).
% 0.55/0.67 tff(517,plain,
% 0.55/0.67 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7)),
% 0.55/0.67 inference(monotonicity,[status(thm)],[402])).
% 0.55/0.67 tff(518,plain,
% 0.55/0.67 (nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))),
% 0.55/0.67 inference(symmetry,[status(thm)],[517])).
% 0.55/0.67 tff(519,plain,
% 0.55/0.67 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.67 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.67 tff(520,plain,
% 0.55/0.67 ($lesseq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[519, 518])).
% 0.55/0.68 tff(521,plain,
% 0.55/0.68 ((~(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7) = nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))) | $greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.68 inference(theory_lemma,[status(thm)],[])).
% 0.55/0.68 tff(522,plain,
% 0.55/0.68 ($greatereq($sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, C!7), $product(-1, nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(I!4), get(color1, int, t2tb(A!5), t2tb2(J!3)))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), 0)),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[521, 518])).
% 0.55/0.68 tff(523,plain,
% 0.55/0.68 ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = $sum(nb_occ(tb2t(set(color1, int, t2tb(A!5), t2tb2(tb2t2(t2tb2(I!4))), t2tb1(tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))))), K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3)))), $product(-1, nb_occ(A!5, K1!9, K2!8, tb2t1(get(color1, int, t2tb(A!5), t2tb2(J!3))))))),
% 0.55/0.68 inference(theory_lemma,[status(thm)],[446, 406, 410, 448, 522, 520, 516, 514, 503, 501])).
% 0.55/0.68 tff(524,plain,
% 0.55/0.68 ($sum(nb_occ(A2!6, K1!9, K2!8, C!7), $product(-1, nb_occ(A!5, K1!9, K2!8, C!7))) = 0),
% 0.55/0.68 inference(transitivity,[status(thm)],[523, 491])).
% 0.55/0.68 tff(525,plain,
% 0.55/0.68 ($false),
% 0.55/0.68 inference(unit_resolution,[status(thm)],[281, 524])).
% 0.55/0.68 % SZS output end Proof
%------------------------------------------------------------------------------