TSTP Solution File: SWW591_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW591_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:22 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW591_2 : TPTP v8.1.0. Released v6.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 21:18:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(tb2t2_type, type, (
% 0.19/0.45 tb2t2: uni > $int)).
% 0.19/0.45 tff(t2tb2_type, type, (
% 0.19/0.45 t2tb2: $int > uni)).
% 0.19/0.45 tff(fib_type, type, (
% 0.19/0.45 fib: $int > $int)).
% 0.19/0.45 tff(tptp_fun_N_3_type, type, (
% 0.19/0.45 tptp_fun_N_3: $int)).
% 0.19/0.45 tff(tptp_fun_X_1_type, type, (
% 0.19/0.45 tptp_fun_X_1: map_int_lpoption_intrp > $int)).
% 0.19/0.45 tff(tb2t_type, type, (
% 0.19/0.45 tb2t: uni > map_int_lpoption_intrp)).
% 0.19/0.45 tff(set_type, type, (
% 0.19/0.45 set: ( ty * ty * uni * uni * uni ) > uni)).
% 0.19/0.45 tff(some_type, type, (
% 0.19/0.45 some: ( ty * uni ) > uni)).
% 0.19/0.45 tff(int_type, type, (
% 0.19/0.45 int: ty)).
% 0.19/0.45 tff(t2tb_type, type, (
% 0.19/0.45 t2tb: map_int_lpoption_intrp > uni)).
% 0.19/0.45 tff(tptp_fun_Table1_4_type, type, (
% 0.19/0.45 tptp_fun_Table1_4: map_int_lpoption_intrp)).
% 0.19/0.45 tff(option_type, type, (
% 0.19/0.45 option: ty > ty)).
% 0.19/0.45 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.45 tptp_fun_Y_0: map_int_lpoption_intrp > $int)).
% 0.19/0.45 tff(some_proj_1_type, type, (
% 0.19/0.45 some_proj_1: ( ty * uni ) > uni)).
% 0.19/0.45 tff(sort_type, type, (
% 0.19/0.45 sort: ( ty * uni ) > $o)).
% 0.19/0.45 tff(t2tb1_type, type, (
% 0.19/0.45 t2tb1: option_int > uni)).
% 0.19/0.45 tff(tb2t1_type, type, (
% 0.19/0.45 tb2t1: uni > option_int)).
% 0.19/0.45 tff(get_type, type, (
% 0.19/0.45 get: ( ty * ty * uni * uni ) > uni)).
% 0.19/0.45 tff(inv_type, type, (
% 0.19/0.45 inv: map_int_lpoption_intrp > $o)).
% 0.19/0.45 tff(tptp_fun_Table2_5_type, type, (
% 0.19/0.45 tptp_fun_Table2_5: map_int_lpoption_intrp)).
% 0.19/0.45 tff(none_type, type, (
% 0.19/0.45 none: ty > uni)).
% 0.19/0.45 tff(tptp_fun_Table_2_type, type, (
% 0.19/0.45 tptp_fun_Table_2: map_int_lpoption_intrp)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 (^[I: $int] : refl(($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0) <=> ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (^[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)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (^[I: $int] : rewrite((tb2t2(t2tb2(I)) = I) <=> ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (![I: $int] : (tb2t2(t2tb2(I)) = I) <=> ![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![I: $int] : (tb2t2(t2tb2(I)) = I) <=> ![I: $int] : (tb2t2(t2tb2(I)) = I)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(8,axiom,(![I: $int] : (tb2t2(t2tb2(I)) = I)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeL2')).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (![I: $int] : (tb2t2(t2tb2(I)) = I)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (![I: $int] : ($sum(tb2t2(t2tb2(I)), $product(-1, I)) = 0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.19/0.45 tff(12,plain,(
% 0.19/0.45 ![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.45 inference(skolemize,[status(sab)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))) = 0)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 ($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))) = 0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 ((~($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))) = 0)) | $greatereq($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))), 0)),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 ($greatereq($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 ((~($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))) = 0)) | $lesseq($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))), 0)),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 ($lesseq($sum(fib(N!3), $product(-1, tb2t2(t2tb2(fib(N!3))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[18, 15])).
% 0.19/0.45 tff(20,assumption,(~$greatereq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)), introduced(assumption)).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[21, 13])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 ((~($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0)) | $greatereq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 ($greatereq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (^[X: $int] : refl(sort(int, t2tb2(X)) <=> sort(int, t2tb2(X)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![X: $int] : sort(int, t2tb2(X)) <=> ![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (![X: $int] : sort(int, t2tb2(X)) <=> ![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(28,axiom,(![X: $int] : sort(int, t2tb2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2tb_sort2')).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.45 tff(30,plain,(
% 0.19/0.45 ![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.45 inference(skolemize,[status(sab)],[29])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 (![X: $int] : sort(int, t2tb2(X))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 ((~![X: $int] : sort(int, t2tb2(X))) | sort(int, t2tb2(fib(N!3)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (sort(int, t2tb2(fib(N!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (^[A: ty, U: uni] : refl(((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U)) <=> ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U)) <=> ![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U)) <=> ![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (^[A: ty, U: uni] : rewrite((sort(A, U) => (some_proj_1(A, some(A, U)) = U)) <=> ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (![A: ty, U: uni] : (sort(A, U) => (some_proj_1(A, some(A, U)) = U)) <=> ![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.45 tff(39,axiom,(![A: ty, U: uni] : (sort(A, U) => (some_proj_1(A, some(A, U)) = U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','some_proj_1_def')).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.45 tff(42,plain,(
% 0.19/0.45 ![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(skolemize,[status(sab)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | ((~sort(int, t2tb2(fib(N!3)))) | (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = t2tb2(fib(N!3))))) <=> ((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | (~sort(int, t2tb2(fib(N!3)))) | (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = t2tb2(fib(N!3))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 ((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | ((~sort(int, t2tb2(fib(N!3)))) | (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = t2tb2(fib(N!3))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | (~sort(int, t2tb2(fib(N!3)))) | (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = t2tb2(fib(N!3)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 ((~sort(int, t2tb2(fib(N!3)))) | (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = t2tb2(fib(N!3)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = t2tb2(fib(N!3))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(51,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR1')).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.45 tff(53,plain,(
% 0.19/0.45 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.19/0.45 inference(skolemize,[status(sab)],[52])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (t2tb1(tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (^[T: map_int_lpoption_intrp] : refl((~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))) <=> (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))) <=> ![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (^[T: map_int_lpoption_intrp] : rewrite((~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))) <=> (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))) <=> ![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))) <=> ![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (^[T: map_int_lpoption_intrp] : trans(monotonicity(rewrite(((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) <=> ((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))), ((((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) & (inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))) <=> (((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) & (inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))))), rewrite((((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) & (inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))) <=> (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))), ((((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) & (inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))) <=> (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) & (inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0))))) <=> ![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (^[T: map_int_lpoption_intrp] : rewrite((inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X)))) <=> (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X)))) <=> ![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X)))) <=> ![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (^[T: map_int_lpoption_intrp] : rewrite((inv(T) <=> ![X: $int, Y: $int] : ((tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y)))) => (Y = fib(X)))) <=> (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y)))) => (Y = fib(X)))) <=> ![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.46 tff(69,axiom,(![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y)))) => (Y = fib(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inv_def')).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | (Y = fib(X))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (inv(T) <=> ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[71, 65])).
% 0.19/0.46 tff(73,plain,(
% 0.19/0.46 ![T: map_int_lpoption_intrp] : (((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) & (inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[72])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[74, 61])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 ((~![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))) | (~((~((~inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (~((~((~inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (((~((~inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)))))) | (inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (((inv(Table1!4) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) & ($greatereq(N!3, 0) & inv(Table!2)) & (tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int)))) <=> (inv(Table1!4) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) & $greatereq(N!3, 0) & inv(Table!2) & (tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 ((~(~(tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int))))) <=> (tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 ((~(~($greatereq(N!3, 0) & inv(Table!2)))) <=> ($greatereq(N!3, 0) & inv(Table!2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (((~(~inv(Table1!4))) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) <=> (inv(Table1!4) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 ((((~(~inv(Table1!4))) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) & (~(~($greatereq(N!3, 0) & inv(Table!2)))) & (~(~(tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int)))))) <=> ((inv(Table1!4) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) & ($greatereq(N!3, 0) & inv(Table!2)) & (tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[83, 82, 81])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 ((((~(~inv(Table1!4))) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) & (~(~($greatereq(N!3, 0) & inv(Table!2)))) & (~(~(tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int)))))) <=> (inv(Table1!4) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) & $greatereq(N!3, 0) & inv(Table!2) & (tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[84, 80])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 ((~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~($greatereq(N, 0) & inv(Table))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))))) <=> (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~($greatereq(N, 0) & inv(Table))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 ((~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table))))) <=> (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~($greatereq(N, 0) & inv(Table))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 ((~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table))))) <=> (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 ((~![N: $int, Table: map_int_lpoption_intrp] : (($lesseq(0, N) & inv(Table)) => ((tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int))) => (($lesseq(0, N) & inv(Table)) => ![Table1: map_int_lpoption_intrp] : (inv(Table1) => ![Table2: map_int_lpoption_intrp] : ((Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N)))))) => ((fib(N) = fib(N)) & inv(Table2)))))))) <=> (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(90,axiom,(~![N: $int, Table: map_int_lpoption_intrp] : (($lesseq(0, N) & inv(Table)) => ((tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int))) => (($lesseq(0, N) & inv(Table)) => ![Table1: map_int_lpoption_intrp] : (inv(Table1) => ![Table2: map_int_lpoption_intrp] : ((Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N)))))) => ((fib(N) = fib(N)) & inv(Table2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_memo_fibo')).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))) | (~($lesseq(0, N) & inv(Table))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~($greatereq(N, 0) & inv(Table))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~($greatereq(N, 0) & inv(Table))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[95, 86])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (~![N: $int, Table: map_int_lpoption_intrp] : (![Table1: map_int_lpoption_intrp] : ((~inv(Table1)) | ![Table2: map_int_lpoption_intrp] : (inv(Table2) | (~(Table2 = tb2t(set(option(int), int, t2tb(Table1), t2tb2(N), some(int, t2tb2(fib(N))))))))) | (~($greatereq(N, 0) & inv(Table))) | (~(tb2t1(get(option(int), int, t2tb(Table), t2tb2(N))) = tb2t1(none(int)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (inv(Table1!4) & (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) & $greatereq(N!3, 0) & inv(Table!2) & (tb2t1(get(option(int), int, t2tb(Table!2), t2tb2(N!3))) = tb2t1(none(int)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[97, 85])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (~(inv(Table2!5) | (~(Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[98])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (Table2!5 = tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))),
% 0.19/0.47 inference(or_elim,[status(thm)],[99])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))) = Table2!5),
% 0.19/0.47 inference(symmetry,[status(thm)],[100])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) <=> inv(Table2!5)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (inv(Table2!5) <=> inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))),
% 0.19/0.47 inference(symmetry,[status(thm)],[102])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~inv(Table2!5)) <=> (~inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (~inv(Table2!5)),
% 0.19/0.47 inference(or_elim,[status(thm)],[99])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (~inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 ((~(inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))))) | inv(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) | (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (~((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[107, 106, 79])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)) | (tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (t2tb1(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = t2tb1(tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 (t2tb1(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 54])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = t2tb1(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.48 inference(symmetry,[status(thm)],[113])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(117,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR')).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,plain,(
% 0.19/0.48 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.48 inference(skolemize,[status(sab)],[118])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) = set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) = set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))) = t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))),
% 0.19/0.48 inference(symmetry,[status(thm)],[122])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.19/0.48 tff(125,assumption,(get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), introduced(assumption)).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.48 inference(symmetry,[status(thm)],[125])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[126, 124, 114, 111, 56])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (((~(tb2t1(get(option(int), int, t2tb(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)) | (~($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 (~($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[129, 108])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 ((~![T: map_int_lpoption_intrp] : (~((~((~inv(T)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(T) | (~((~(tb2t1(get(option(int), int, t2tb(T), t2tb2(tptp_fun_X_1(T)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(T)))))) | ($sum(tptp_fun_Y_0(T), $product(-1, fib(tptp_fun_X_1(T)))) = 0)))))))) | (~((~((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(Table1!4) | (~((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(Table1!4)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(Table1!4)))))) | ($sum(tptp_fun_Y_0(Table1!4), $product(-1, fib(tptp_fun_X_1(Table1!4)))) = 0)))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 (~((~((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(Table1!4) | (~((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(Table1!4)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(Table1!4)))))) | ($sum(tptp_fun_Y_0(Table1!4), $product(-1, fib(tptp_fun_X_1(Table1!4)))) = 0))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[131, 75])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 (((~((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~(inv(Table1!4) | (~((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(Table1!4)))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(Table1!4)))))) | ($sum(tptp_fun_Y_0(Table1!4), $product(-1, fib(tptp_fun_X_1(Table1!4)))) = 0)))))) | ((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 ((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (inv(Table1!4)),
% 0.19/0.48 inference(and_elim,[status(thm)],[98])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 ((~((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | (~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 ((~((~inv(Table1!4)) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0)))) | ![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 (((~![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) | ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))) <=> ((~![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) | (~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 ((~![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) | ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 ((~![X: $int, Y: $int] : ((~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(X))) = tb2t1(some(int, t2tb2(Y))))) | ($sum(Y, $product(-1, fib(X))) = 0))) | (~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 (~(tb2t1(get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = tb2t1(some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[141, 138, 130])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[142, 128])).
% 0.19/0.49 tff(144,plain,(~(get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 ((~![X: $int] : sort(int, t2tb2(X))) | sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[145, 31])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 ((~![X: $int] : sort(int, t2tb2(X))) | sort(int, t2tb2(N!3))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 (sort(int, t2tb2(N!3))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[147, 31])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[154, 152])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (^[A: ty, B: ty, M: uni, A1: uni, A2: uni] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B1: uni] : rewrite(((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), (![B1: uni] : ((~(A1 = A2)) => (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))) <=> ![B1: uni] : ((A1 = A2) | (get(B, A, set(B, A, M, A1, B1), A2) = get(B, A, M, A2))))), ((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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.49 tff(159,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/sandbox2/benchmark/theBenchmark.p','select_neq')).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.19/0.49 tff(162,plain,(
% 0.19/0.49 ![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)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[161])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[163, 150])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 (((~![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(N!3))) | (~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!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(N!3))) | (~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 (((~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(int, t2tb2(N!3))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) <=> ((~sort(int, t2tb2(N!3))) | (~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(167,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(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(int, t2tb2(N!3))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!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(N!3))) | (~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[166])).
% 0.19/0.50 tff(168,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(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(int, t2tb2(N!3))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!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(N!3))) | (~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[167, 165])).
% 0.19/0.50 tff(169,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(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(int, t2tb2(N!3))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(170,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(N!3))) | (~sort(int, t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | ![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 (![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[170, 164, 148, 146])).
% 0.19/0.50 tff(172,plain,
% 0.19/0.50 (((~![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) <=> ((~![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | (t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(173,plain,
% 0.19/0.50 ((~![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 ((~![B1: uni] : ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), B1), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))) | (t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 ((t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = get(option(int), int, t2tb(Table1!4), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[174, 171])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 (t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[175, 144])).
% 0.19/0.50 tff(177,plain,
% 0.19/0.50 (^[A: ty, X: uni] : refl(sort(option(A), some(A, X)) <=> sort(option(A), some(A, X)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (![A: ty, X: uni] : sort(option(A), some(A, X)) <=> ![A: ty, X: uni] : sort(option(A), some(A, X))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[177])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (![A: ty, X: uni] : sort(option(A), some(A, X)) <=> ![A: ty, X: uni] : sort(option(A), some(A, X))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(180,axiom,(![A: ty, X: uni] : sort(option(A), some(A, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','some_sort')).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 (![A: ty, X: uni] : sort(option(A), some(A, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.50 tff(182,plain,(
% 0.19/0.50 ![A: ty, X: uni] : sort(option(A), some(A, X))),
% 0.19/0.50 inference(skolemize,[status(sab)],[181])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 (![A: ty, X: uni] : sort(option(A), some(A, X))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 ((~![A: ty, X: uni] : sort(option(A), some(A, X))) | sort(option(int), some(int, t2tb2(fib(N!3))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (sort(option(int), some(int, t2tb2(fib(N!3))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.19/0.50 tff(186,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(187,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)],[186])).
% 0.19/0.50 tff(188,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(189,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(190,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)],[189])).
% 0.19/0.50 tff(191,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/sandbox2/benchmark/theBenchmark.p','select_eq')).
% 0.19/0.50 tff(192,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)],[191, 190])).
% 0.19/0.51 tff(193,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.19/0.51 tff(194,plain,(
% 0.19/0.51 ![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)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[193])).
% 0.19/0.51 tff(195,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.19/0.51 tff(196,plain,
% 0.19/0.51 (((~![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(option(int), some(int, t2tb2(fib(N!3))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!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(option(int), some(int, t2tb2(fib(N!3))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(197,plain,
% 0.19/0.51 (((get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(option(int), some(int, t2tb2(fib(N!3)))))) <=> ((~sort(option(int), some(int, t2tb2(fib(N!3))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(198,plain,
% 0.19/0.51 (((~![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(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(option(int), some(int, t2tb2(fib(N!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(option(int), some(int, t2tb2(fib(N!3))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.51 tff(199,plain,
% 0.19/0.51 (((~![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(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(option(int), some(int, t2tb2(fib(N!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(option(int), some(int, t2tb2(fib(N!3))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.51 tff(200,plain,
% 0.19/0.51 ((~![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(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (~sort(option(int), some(int, t2tb2(fib(N!3))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(201,plain,
% 0.19/0.51 ((~![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(option(int), some(int, t2tb2(fib(N!3))))) | (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.51 tff(202,plain,
% 0.19/0.51 ((get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))) | (~(t2tb2(N!3) = t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[201, 195, 185])).
% 0.19/0.51 tff(203,plain,
% 0.19/0.51 (get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = some(int, t2tb2(fib(N!3)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[202, 176])).
% 0.19/0.51 tff(204,plain,
% 0.19/0.51 (some(int, t2tb2(fib(N!3))) = get(option(int), int, set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))), t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[203])).
% 0.19/0.51 tff(205,plain,
% 0.19/0.51 (some(int, t2tb2(fib(N!3))) = some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[204, 124, 114, 111, 56])).
% 0.19/0.51 tff(206,plain,
% 0.19/0.51 (some_proj_1(int, some(int, t2tb2(fib(N!3)))) = some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[205])).
% 0.19/0.51 tff(207,plain,
% 0.19/0.51 (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = some_proj_1(int, some(int, t2tb2(fib(N!3))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[206])).
% 0.19/0.51 tff(208,plain,
% 0.19/0.51 ((~![X: $int] : sort(int, t2tb2(X))) | sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(209,plain,
% 0.19/0.51 (sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[208, 31])).
% 0.19/0.51 tff(210,plain,
% 0.19/0.51 (((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | ((~sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) <=> ((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | (~sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(211,plain,
% 0.19/0.51 ((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | ((~sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(212,plain,
% 0.19/0.51 ((~![A: ty, U: uni] : ((~sort(A, U)) | (some_proj_1(A, some(A, U)) = U))) | (~sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.19/0.51 tff(213,plain,
% 0.19/0.51 ((~sort(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[212, 43])).
% 0.19/0.51 tff(214,plain,
% 0.19/0.51 (some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[213, 209])).
% 0.19/0.51 tff(215,plain,
% 0.19/0.51 (t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))) = some_proj_1(int, some(int, t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[214])).
% 0.19/0.51 tff(216,plain,
% 0.19/0.51 (t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))) = t2tb2(fib(N!3))),
% 0.19/0.51 inference(transitivity,[status(thm)],[215, 207, 48])).
% 0.19/0.51 tff(217,plain,
% 0.19/0.51 (tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = tb2t2(t2tb2(fib(N!3)))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.51 tff(218,plain,
% 0.19/0.51 (tb2t2(t2tb2(fib(N!3))) = tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(symmetry,[status(thm)],[217])).
% 0.19/0.51 tff(219,plain,
% 0.19/0.51 ((~(tb2t2(t2tb2(fib(N!3))) = tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) | $lesseq($sum(tb2t2(t2tb2(fib(N!3))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51 tff(220,plain,
% 0.19/0.51 ($lesseq($sum(tb2t2(t2tb2(fib(N!3))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.19/0.51 tff(221,plain,
% 0.19/0.51 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))) = 0)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(222,plain,
% 0.19/0.51 ($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))) = 0),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[221, 13])).
% 0.19/0.51 tff(223,plain,
% 0.19/0.51 ((~($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))) = 0)) | $lesseq($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))), 0)),
% 0.19/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51 tff(224,plain,
% 0.19/0.51 ($lesseq($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))), 0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.19/0.51 tff(225,plain,
% 0.19/0.51 ((~($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))) = 0)) | $greatereq($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))), 0)),
% 0.19/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51 tff(226,plain,
% 0.19/0.51 ($greatereq($sum(N!3, $product(-1, tb2t2(t2tb2(N!3)))), 0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[225, 222])).
% 0.19/0.51 tff(227,plain,
% 0.19/0.51 (N!3 = tb2t2(t2tb2(N!3))),
% 0.19/0.51 inference(theory_lemma,[status(thm)],[226, 224])).
% 0.19/0.51 tff(228,plain,
% 0.19/0.51 (tb2t2(t2tb2(N!3)) = N!3),
% 0.19/0.51 inference(symmetry,[status(thm)],[227])).
% 0.19/0.51 tff(229,plain,
% 0.19/0.51 (tb2t2(t2tb2(N!3)) = tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[176])).
% 0.19/0.51 tff(230,plain,
% 0.19/0.51 (tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))) = tb2t2(t2tb2(N!3))),
% 0.19/0.51 inference(symmetry,[status(thm)],[229])).
% 0.19/0.51 tff(231,plain,
% 0.19/0.51 ((~![I: $int] : ($sum(I, $product(-1, tb2t2(t2tb2(I)))) = 0)) | ($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(232,plain,
% 0.19/0.51 ($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[231, 13])).
% 0.19/0.51 tff(233,plain,
% 0.19/0.51 ((~($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0)) | $lesseq($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51 tff(234,plain,
% 0.19/0.51 ($lesseq($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.19/0.51 tff(235,plain,
% 0.19/0.51 ((~($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0)) | $greatereq($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(236,plain,
% 0.19/0.52 ($greatereq($sum(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[235, 232])).
% 0.19/0.52 tff(237,plain,
% 0.19/0.52 (tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) = tb2t2(t2tb2(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[236, 234])).
% 0.19/0.52 tff(238,plain,
% 0.19/0.52 (tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))) = N!3),
% 0.19/0.52 inference(transitivity,[status(thm)],[237, 230, 228])).
% 0.19/0.52 tff(239,plain,
% 0.19/0.52 (fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))) = fib(N!3)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[238])).
% 0.19/0.52 tff(240,plain,
% 0.19/0.52 (fib(N!3) = fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))),
% 0.19/0.52 inference(symmetry,[status(thm)],[239])).
% 0.19/0.52 tff(241,plain,
% 0.19/0.52 ((~(fib(N!3) = fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | $greatereq($sum(fib(N!3), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(242,plain,
% 0.19/0.52 ($greatereq($sum(fib(N!3), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.19/0.52 tff(243,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[242, 220, 24, 20, 19])).
% 0.19/0.52 tff(244,plain,($greatereq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(245,plain,
% 0.19/0.52 (($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) = 0) | (~$lesseq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)) | (~$greatereq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0))),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(246,plain,
% 0.19/0.52 ((~$lesseq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)) | (~$greatereq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[245, 130])).
% 0.19/0.52 tff(247,plain,
% 0.19/0.52 (~$lesseq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[246, 244])).
% 0.19/0.52 tff(248,plain,
% 0.19/0.52 ((~($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) = 0)) | $lesseq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(249,plain,
% 0.19/0.52 ($lesseq($sum(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[248, 22])).
% 0.19/0.52 tff(250,plain,
% 0.19/0.52 ((~(tb2t2(t2tb2(fib(N!3))) = tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))) | $greatereq($sum(tb2t2(t2tb2(fib(N!3))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(251,plain,
% 0.19/0.52 ($greatereq($sum(tb2t2(t2tb2(fib(N!3))), $product(-1, tb2t2(t2tb2(tptp_fun_Y_0(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3)))))))))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[250, 218])).
% 0.19/0.52 tff(252,plain,
% 0.19/0.52 ((~(fib(N!3) = fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))) | $lesseq($sum(fib(N!3), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.52 tff(253,plain,
% 0.19/0.52 ($lesseq($sum(fib(N!3), $product(-1, fib(tptp_fun_X_1(tb2t(set(option(int), int, t2tb(Table1!4), t2tb2(N!3), some(int, t2tb2(fib(N!3))))))))), 0)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[252, 240])).
% 0.19/0.52 tff(254,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(theory_lemma,[status(thm)],[253, 251, 249, 247, 17])).
% 0.19/0.52 % SZS output end Proof
%------------------------------------------------------------------------------