TSTP Solution File: SWW626_2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW626_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 20:59:29 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW626_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 20:25:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(permut_type, type, (
% 0.20/0.47 permut: ( ty * uni * uni ) > $o)).
% 0.20/0.47 tff(infix_plpl_type, type, (
% 0.20/0.47 infix_plpl: ( ty * uni * uni ) > uni)).
% 0.20/0.47 tff(t2tb_type, type, (
% 0.20/0.47 t2tb: list_elt > uni)).
% 0.20/0.47 tff(tptp_fun_S2_15_type, type, (
% 0.20/0.47 tptp_fun_S2_15: list_elt)).
% 0.20/0.47 tff(tptp_fun_S1_14_type, type, (
% 0.20/0.47 tptp_fun_S1_14: list_elt)).
% 0.20/0.47 tff(elt1_type, type, (
% 0.20/0.47 elt1: ty)).
% 0.20/0.47 tff(prefix_type, type, (
% 0.20/0.47 prefix: ( ty * $int * uni ) > uni)).
% 0.20/0.47 tff(tptp_fun_L2_13_type, type, (
% 0.20/0.47 tptp_fun_L2_13: list_elt)).
% 0.20/0.47 tff(div_type, type, (
% 0.20/0.47 div: ( $int * $int ) > $int)).
% 0.20/0.47 tff(tptp_fun_N_12_type, type, (
% 0.20/0.47 tptp_fun_N_12: $int)).
% 0.20/0.47 tff(tptp_fun_L_11_type, type, (
% 0.20/0.47 tptp_fun_L_11: list_elt)).
% 0.20/0.47 tff(nil_type, type, (
% 0.20/0.47 nil: ty > uni)).
% 0.20/0.47 tff(cons_type, type, (
% 0.20/0.47 cons: ( ty * uni * uni ) > uni)).
% 0.20/0.47 tff(tptp_fun_Result_16_type, type, (
% 0.20/0.47 tptp_fun_Result_16: list_elt)).
% 0.20/0.47 tff(tb2t_type, type, (
% 0.20/0.47 tb2t: uni > list_elt)).
% 0.20/0.47 tff(length_type, type, (
% 0.20/0.47 length: ( ty * uni ) > $int)).
% 0.20/0.47 tff(mem_type, type, (
% 0.20/0.47 mem: ( ty * uni * uni ) > $o)).
% 0.20/0.47 tff(t2tb1_type, type, (
% 0.20/0.47 t2tb1: elt > uni)).
% 0.20/0.47 tff(le_type, type, (
% 0.20/0.47 le: ( elt * elt ) > $o)).
% 0.20/0.47 tff(sorted_type, type, (
% 0.20/0.47 sorted: list_elt > $o)).
% 0.20/0.47 tff(reverse_type, type, (
% 0.20/0.47 reverse: ( ty * uni ) > uni)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[A: ty, L2: uni] : refl((~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))) <=> (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))) <=> ![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (^[A: ty, L2: uni] : rewrite((~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))) <=> (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))) <=> ![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))) <=> ![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (^[A: ty, L2: uni] : rewrite(((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))) <=> (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![A: ty, L2: uni] : ((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))) <=> ![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (![A: ty, L2: uni] : ((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2)))) <=> ![A: ty, L2: uni] : ((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(9,axiom,(![A: ty, L2: uni] : ((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','infix_plpl_def')).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (![A: ty, L2: uni] : ((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.47 tff(11,plain,(
% 0.20/0.47 ![A: ty, L2: uni] : ((infix_plpl(A, nil(A), L2) = L2) & ![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[10])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 ((~![A: ty, L2: uni] : (~((~(infix_plpl(A, nil(A), L2) = L2)) | (~![X: uni, X1: uni] : (infix_plpl(A, cons(A, X, X1), L2) = cons(A, X, infix_plpl(A, X1, L2))))))) | (~((~(infix_plpl(elt1, nil(elt1), t2tb(S1!14)) = t2tb(S1!14))) | (~![X: uni, X1: uni] : (infix_plpl(elt1, cons(elt1, X, X1), t2tb(S1!14)) = cons(elt1, X, infix_plpl(elt1, X1, t2tb(S1!14)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (~((~(infix_plpl(elt1, nil(elt1), t2tb(S1!14)) = t2tb(S1!14))) | (~![X: uni, X1: uni] : (infix_plpl(elt1, cons(elt1, X, X1), t2tb(S1!14)) = cons(elt1, X, infix_plpl(elt1, X1, t2tb(S1!14))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (((~(infix_plpl(elt1, nil(elt1), t2tb(S1!14)) = t2tb(S1!14))) | (~![X: uni, X1: uni] : (infix_plpl(elt1, cons(elt1, X, X1), t2tb(S1!14)) = cons(elt1, X, infix_plpl(elt1, X1, t2tb(S1!14)))))) | (infix_plpl(elt1, nil(elt1), t2tb(S1!14)) = t2tb(S1!14))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (infix_plpl(elt1, nil(elt1), t2tb(S1!14)) = t2tb(S1!14)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (t2tb(S1!14) = infix_plpl(elt1, nil(elt1), t2tb(S1!14))),
% 0.20/0.47 inference(symmetry,[status(thm)],[17])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15)) = infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))) <=> permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))) <=> permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[20])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 ((~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))) <=> (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(25,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.47 tff(27,plain,(
% 0.20/0.47 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.20/0.47 inference(skolemize,[status(sab)],[26])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(prefix(elt1, N!12, t2tb(L!11)))) = prefix(elt1, N!12, t2tb(L!11)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (t2tb(tb2t(prefix(elt1, N!12, t2tb(L!11)))) = prefix(elt1, N!12, t2tb(L!11))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (((~(N!12 = 3)) & (~(N!12 = 2)) & ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))) & ($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)) & ($greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0))) <=> ((~(N!12 = 3)) & (~(N!12 = 2)) & (~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))) & $greatereq(div(N!12, 2), 0) & $greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 ((~(~($greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0)))) <=> ($greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 ((~(~($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)))) <=> ($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 ((~($greatereq(div(N!12, 2), 0) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0))) <=> (~($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 ((~(~($greatereq(div(N!12, 2), 0) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) <=> (~(~($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~(~($greatereq(div(N!12, 2), 0) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) <=> ($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))) & ($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ((~(~(L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))))) <=> (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 ((~(~(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))))) <=> (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~(~($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)))) <=> ($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0))) <=> (~($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 ((~(~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) <=> (~(~($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 ((~(~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) <=> ($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) & ($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0)) & (sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 ((~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))))) <=> (sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 ((~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0)))) <=> ($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 ((~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0))) <=> (~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ((~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) <=> (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 ((~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) <=> ($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0))),
% 0.20/0.48 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))))) & (sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))))) <=> (sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 ((sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) <=> (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))))) & (sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[52, 51])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[53, 50])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) & (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) & (~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))))) <=> (((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) & ($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0)) & (sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[54, 49, 45])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 ((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) & (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) & (~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[55, 44])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) & (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) & (~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))))) & (~(~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) & (~(~(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))))) & (~(~(L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))))) <=> (((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))) & ($greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[56, 43, 39, 38])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) & (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) & (~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))))) & (~(~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) & (~(~(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))))) & (~(~(L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))))) <=> ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[57, 37])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (((~(N!12 = 3)) & (~(N!12 = 2)) & ((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) & (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) & (~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))))) & (~(~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) & (~(~(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))))) & (~(~(L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))))) & (~(~($greatereq(div(N!12, 2), 0) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) & (~(~($greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0))))) <=> ((~(N!12 = 3)) & (~(N!12 = 2)) & ((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))) & ($greatereq(div(N!12, 2), 0) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0)) & ($greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[58, 36, 32])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (((~(N!12 = 3)) & (~(N!12 = 2)) & ((((~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & (sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1!14))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2!15))) | (~mem(elt1, t2tb1(X), nil(elt1))))) & (~(~(sorted(S2!15) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))))) & (~(~($greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, length(elt1, t2tb(L2!13))), $product(-1, div(N!12, 2)))), 0)))) & (~(~(sorted(S1!14) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))))))) & (~(~($greatereq(div(N!12, 2), 2) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) & (~(~(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))))) & (~(~(L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13))))))) & (~(~($greatereq(div(N!12, 2), 0) & $greatereq($sum(length(elt1, t2tb(L!11)), $product(-1, div(N!12, 2))), 0)))) & (~(~($greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0))))) <=> ((~(N!12 = 3)) & (~(N!12 = 2)) & (~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))) & $greatereq(div(N!12, 2), 0) & $greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0))),
% 0.20/0.49 inference(transitivity,[status(thm)],[59, 31])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 ((~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : (![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, length(elt1, t2tb(L2))), $product(-1, div(N, 2)))), 0))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))))) | (~($greatereq(div(N, 2), 2) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))))) | (~($greatereq(div(N, 2), 0) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))))) <=> (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : (![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, length(elt1, t2tb(L2))), $product(-1, div(N, 2)))), 0))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))))) | (~($greatereq(div(N, 2), 2) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))))) | (~($greatereq(div(N, 2), 0) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 ((~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, div(N, 2)), $product(-1, length(elt1, t2tb(L2))))), 0)))) | (~($greatereq(div(N, 2), 2) & $lesseq($sum(div(N, 2), $product(-1, length(elt1, t2tb(L)))), 0)))) | (~($greatereq(div(N, 2), 0) & $lesseq($sum(div(N, 2), $product(-1, length(elt1, t2tb(L)))), 0))))) <=> (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : (![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, length(elt1, t2tb(L2))), $product(-1, div(N, 2)))), 0))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))))) | (~($greatereq(div(N, 2), 2) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))))) | (~($greatereq(div(N, 2), 0) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 ((~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L))))))) <=> (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, div(N, 2)), $product(-1, length(elt1, t2tb(L2))))), 0)))) | (~($greatereq(div(N, 2), 2) & $lesseq($sum(div(N, 2), $product(-1, length(elt1, t2tb(L)))), 0)))) | (~($greatereq(div(N, 2), 0) & $lesseq($sum(div(N, 2), $product(-1, length(elt1, t2tb(L)))), 0)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(64,plain,
% 0.20/0.50 ((~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L))))))) <=> (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(65,plain,
% 0.20/0.50 ((~![N: $int, L: list_elt] : (($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L)))) => ((~(N = 2)) => ((~(N = 3)) => ((~(2 = 0)) => (($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))) => ![L2: list_elt] : ((L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))) => ((tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $difference(N, div(N, 2)), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L)))) => (($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))) => ![S1: list_elt] : ((sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))) => (($lesseq(2, $difference(N, div(N, 2))) & $lesseq($difference(N, div(N, 2)), length(elt1, t2tb(L2)))) => ![S2: list_elt] : ((sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $difference(N, div(N, 2)), t2tb(L2)))) => (((((sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1)) & sorted(S2)) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), nil(elt1)) => (mem(elt1, t2tb1(Y), t2tb(S1)) => le(X, Y)))) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), nil(elt1)) => (mem(elt1, t2tb1(Y), t2tb(S2)) => le(X, Y)))) => ![Result: list_elt] : ((sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2)))) => permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L))))))))))))))))) <=> (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(66,axiom,(~![N: $int, L: list_elt] : (($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L)))) => ((~(N = 2)) => ((~(N = 3)) => ((~(2 = 0)) => (($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))) => ![L2: list_elt] : ((L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))) => ((tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $difference(N, div(N, 2)), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L)))) => (($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))) => ![S1: list_elt] : ((sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))) => (($lesseq(2, $difference(N, div(N, 2))) & $lesseq($difference(N, div(N, 2)), length(elt1, t2tb(L2)))) => ![S2: list_elt] : ((sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $difference(N, div(N, 2)), t2tb(L2)))) => (((((sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1)) & sorted(S2)) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), nil(elt1)) => (mem(elt1, t2tb1(Y), t2tb(S1)) => le(X, Y)))) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), nil(elt1)) => (mem(elt1, t2tb1(Y), t2tb(S2)) => le(X, Y)))) => ![Result: list_elt] : ((sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2)))) => permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_rev_sort')).
% 0.20/0.50 tff(67,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.50 tff(68,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.20/0.50 tff(69,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.50 tff(70,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($lesseq(2, $sum(N, $product(-1, div(N, 2)))) & $lesseq($sum(N, $product(-1, div(N, 2))), length(elt1, t2tb(L2)))))) | (~($lesseq(2, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L)))))) | (~($lesseq(0, div(N, 2)) & $lesseq(div(N, 2), length(elt1, t2tb(L))))) | (~($lesseq(2, N) & $lesseq(N, length(elt1, t2tb(L))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[69, 64])).
% 0.20/0.50 tff(71,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))) | ![L2: list_elt] : ((~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2))))) | ![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, div(N, 2)), $product(-1, length(elt1, t2tb(L2))))), 0)))) | (~($greatereq(div(N, 2), 2) & $lesseq($sum(div(N, 2), $product(-1, length(elt1, t2tb(L)))), 0)))) | (~($greatereq(div(N, 2), 0) & $lesseq($sum(div(N, 2), $product(-1, length(elt1, t2tb(L)))), 0))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.50 tff(72,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : (![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, length(elt1, t2tb(L2))), $product(-1, div(N, 2)))), 0))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))))) | (~($greatereq(div(N, 2), 2) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))))) | (~($greatereq(div(N, 2), 0) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[71, 62])).
% 0.20/0.50 tff(73,plain,
% 0.20/0.50 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : (![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, length(elt1, t2tb(L2))), $product(-1, div(N, 2)))), 0))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))))) | (~($greatereq(div(N, 2), 2) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))))) | (~($greatereq(div(N, 2), 0) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[72, 61])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (~![N: $int, L: list_elt] : ((N = 3) | (N = 2) | ![L2: list_elt] : (![S1: list_elt] : (![S2: list_elt] : (![Result: list_elt] : ((~(sorted(tb2t(reverse(elt1, t2tb(Result)))) & permut(elt1, t2tb(Result), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1)), t2tb(S2))))) | permut(elt1, t2tb(Result), prefix(elt1, N, t2tb(L)))) | (~(sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1) & sorted(S2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S1))) | (~mem(elt1, t2tb1(X), nil(elt1)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(S2))) | (~mem(elt1, t2tb1(X), nil(elt1)))))) | (~(sorted(S2) & permut(elt1, t2tb(S2), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))))) | (~($greatereq($sum(N, $product(-1, div(N, 2))), 2) & $lesseq($sum(N, $sum($product(-1, length(elt1, t2tb(L2))), $product(-1, div(N, 2)))), 0))) | (~(sorted(S1) & permut(elt1, t2tb(S1), prefix(elt1, div(N, 2), t2tb(L)))))) | (~($greatereq(div(N, 2), 2) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~(tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), prefix(elt1, $sum(N, $product(-1, div(N, 2))), t2tb(L2)))) = tb2t(prefix(elt1, N, t2tb(L))))) | (~(L = tb2t(infix_plpl(elt1, prefix(elt1, div(N, 2), t2tb(L)), t2tb(L2)))))) | (~($greatereq(div(N, 2), 0) & $greatereq($sum(length(elt1, t2tb(L)), $product(-1, div(N, 2))), 0))) | (~($greatereq(N, 2) & $lesseq($sum(N, $product(-1, length(elt1, t2tb(L)))), 0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[73, 61])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 ((~(N!12 = 3)) & (~(N!12 = 2)) & (~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) & sorted(tb2t(reverse(elt1, nil(elt1)))) & sorted(S1!14) & sorted(S2!15) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S1!14)))) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(X), nil(elt1))) | (~mem(elt1, t2tb1(Y), t2tb(S2!15)))) & permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) & $greatereq($sum(N!12, $product(-1, div(N!12, 2))), 2) & $lesseq($sum(N!12, $sum($product(-1, div(N!12, 2)), $product(-1, length(elt1, t2tb(L2!13))))), 0) & permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11))) & $greatereq(div(N!12, 2), 2) & $lesseq($sum(div(N!12, 2), $product(-1, length(elt1, t2tb(L!11)))), 0) & (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))) & (L!11 = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(L2!13)))) & $greatereq(div(N!12, 2), 0) & $greatereq(N!12, 2) & $lesseq($sum(N!12, $product(-1, length(elt1, t2tb(L!11)))), 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[74, 60])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 (tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) = tb2t(prefix(elt1, N!12, t2tb(L!11)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[75])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (tb2t(prefix(elt1, N!12, t2tb(L!11))) = tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))),
% 0.20/0.51 inference(symmetry,[status(thm)],[76])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 (t2tb(tb2t(prefix(elt1, N!12, t2tb(L!11)))) = t2tb(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (t2tb(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))) = t2tb(tb2t(prefix(elt1, N!12, t2tb(L!11))))),
% 0.20/0.51 inference(symmetry,[status(thm)],[78])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))) = infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (t2tb(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))))) = infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[80, 28])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 (infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) = t2tb(tb2t(infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))))),
% 0.20/0.51 inference(symmetry,[status(thm)],[81])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))) = prefix(elt1, N!12, t2tb(L!11))),
% 0.20/0.51 inference(transitivity,[status(thm)],[82, 79, 30])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) <=> permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 (permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16)) <=> permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16))),
% 0.20/0.51 inference(symmetry,[status(thm)],[84])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 ((~permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))) <=> (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (~((~(sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))),
% 0.20/0.51 inference(and_elim,[status(thm)],[75])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 (~permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11)))),
% 0.20/0.51 inference(or_elim,[status(thm)],[87])).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 (^[A: ty, L1: uni, L2: uni] : refl(((~permut(A, L1, L2)) | permut(A, L2, L1)) <=> ((~permut(A, L1, L2)) | permut(A, L2, L1)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1)) <=> ![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1)) <=> ![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 (^[A: ty, L1: uni, L2: uni] : rewrite((permut(A, L1, L2) => permut(A, L2, L1)) <=> ((~permut(A, L1, L2)) | permut(A, L2, L1)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni] : (permut(A, L1, L2) => permut(A, L2, L1)) <=> ![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.51 tff(94,axiom,(![A: ty, L1: uni, L2: uni] : (permut(A, L1, L2) => permut(A, L2, L1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_sym')).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.51 tff(97,plain,(
% 0.20/0.51 ![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(skolemize,[status(sab)],[96])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))) | permut(elt1, t2tb(Result!16), prefix(elt1, N!12, t2tb(L!11)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (~permut(elt1, prefix(elt1, N!12, t2tb(L!11)), t2tb(Result!16))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[102, 86])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (sorted(tb2t(reverse(elt1, t2tb(Result!16)))) & permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))),
% 0.20/0.51 inference(or_elim,[status(thm)],[87])).
% 0.20/0.51 tff(105,plain,
% 0.20/0.51 (permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[104])).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))) | permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16)))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))) | permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))) | permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, t2tb(Result!16), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))) | permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[108, 98, 105])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (^[A: ty, L1: uni, L2: uni, L3: uni] : refl((permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2))) <=> (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (^[A: ty, L1: uni, L2: uni, L3: uni] : trans(monotonicity(rewrite((permut(A, L2, L3) => permut(A, L1, L3)) <=> ((~permut(A, L2, L3)) | permut(A, L1, L3))), ((permut(A, L1, L2) => (permut(A, L2, L3) => permut(A, L1, L3))) <=> (permut(A, L1, L2) => ((~permut(A, L2, L3)) | permut(A, L1, L3))))), rewrite((permut(A, L1, L2) => ((~permut(A, L2, L3)) | permut(A, L1, L3))) <=> (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))), ((permut(A, L1, L2) => (permut(A, L2, L3) => permut(A, L1, L3))) <=> (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L2) => (permut(A, L2, L3) => permut(A, L1, L3))) <=> ![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.51 tff(115,axiom,(![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L2) => (permut(A, L2, L3) => permut(A, L1, L3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_trans')).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.51 tff(118,plain,(
% 0.20/0.51 ![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[117])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | ((~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))),
% 0.40/0.51 inference(rewrite,[status(thm)],[])).
% 0.40/0.51 tff(121,plain,
% 0.40/0.51 ((permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))) <=> ((~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))),
% 0.40/0.51 inference(rewrite,[status(thm)],[])).
% 0.40/0.51 tff(122,plain,
% 0.40/0.51 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | ((~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))))),
% 0.40/0.51 inference(monotonicity,[status(thm)],[121])).
% 0.40/0.51 tff(123,plain,
% 0.40/0.51 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))),
% 0.40/0.51 inference(transitivity,[status(thm)],[122, 120])).
% 0.40/0.51 tff(124,plain,
% 0.40/0.52 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(125,plain,
% 0.40/0.52 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt1, infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)), t2tb(Result!16))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.40/0.52 tff(126,plain,
% 0.40/0.52 (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), t2tb(Result!16)) | (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15))))),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[125, 119, 109])).
% 0.40/0.52 tff(127,plain,
% 0.40/0.52 (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, infix_plpl(elt1, nil(elt1), t2tb(S1!14)), t2tb(S2!15)))),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[126, 103])).
% 0.40/0.52 tff(128,plain,
% 0.40/0.52 (~permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15)))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[127, 22])).
% 0.40/0.52 tff(129,plain,
% 0.40/0.52 (permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))),
% 0.40/0.52 inference(and_elim,[status(thm)],[75])).
% 0.40/0.52 tff(130,plain,
% 0.40/0.52 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))) | permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14)))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))) | permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(131,plain,
% 0.40/0.52 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))) | permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(132,plain,
% 0.40/0.52 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, t2tb(S1!14), prefix(elt1, div(N!12, 2), t2tb(L!11)))) | permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.40/0.52 tff(133,plain,
% 0.40/0.52 (permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[132, 98, 129])).
% 0.40/0.52 tff(134,plain,
% 0.40/0.52 (permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))),
% 0.40/0.52 inference(and_elim,[status(thm)],[75])).
% 0.40/0.52 tff(135,plain,
% 0.40/0.52 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) | permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15)))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) | permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(136,plain,
% 0.40/0.52 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) | permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15)))),
% 0.40/0.52 inference(quant_inst,[status(thm)],[])).
% 0.40/0.52 tff(137,plain,
% 0.40/0.52 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt1, t2tb(S2!15), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)))) | permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.40/0.52 tff(138,plain,
% 0.40/0.52 (permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))),
% 0.40/0.52 inference(unit_resolution,[status(thm)],[137, 98, 134])).
% 0.40/0.52 tff(139,plain,
% 0.40/0.52 (^[A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : refl((permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1))) <=> (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1))))),
% 0.40/0.52 inference(bind,[status(th)],[])).
% 0.40/0.52 tff(140,plain,
% 0.40/0.52 (![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1))) <=> ![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(quant_intro,[status(thm)],[139])).
% 0.40/0.52 tff(141,plain,
% 0.40/0.52 (![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1))) <=> ![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(142,plain,
% 0.40/0.52 (^[A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : trans(monotonicity(rewrite((permut(A, L2, K2) => permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2))) <=> ((~permut(A, L2, K2)) | permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)))), ((permut(A, L1, K1) => (permut(A, L2, K2) => permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)))) <=> (permut(A, L1, K1) => ((~permut(A, L2, K2)) | permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)))))), rewrite((permut(A, L1, K1) => ((~permut(A, L2, K2)) | permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)))) <=> (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))), ((permut(A, L1, K1) => (permut(A, L2, K2) => permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)))) <=> (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))))),
% 0.40/0.52 inference(bind,[status(th)],[])).
% 0.40/0.52 tff(143,plain,
% 0.40/0.52 (![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, L1, K1) => (permut(A, L2, K2) => permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)))) <=> ![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(quant_intro,[status(thm)],[142])).
% 0.40/0.52 tff(144,axiom,(![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, L1, K1) => (permut(A, L2, K2) => permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_append')).
% 0.40/0.52 tff(145,plain,
% 0.40/0.52 (![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.40/0.52 tff(146,plain,
% 0.40/0.52 (![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.40/0.52 tff(147,plain,(
% 0.40/0.52 ![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(skolemize,[status(sab)],[146])).
% 0.40/0.52 tff(148,plain,
% 0.40/0.52 (![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))),
% 0.40/0.52 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.40/0.52 tff(149,plain,
% 0.40/0.52 (((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | ((~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))))) <=> ((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(150,plain,
% 0.40/0.52 ((permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14)))) <=> ((~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))))),
% 0.40/0.52 inference(rewrite,[status(thm)],[])).
% 0.40/0.52 tff(151,plain,
% 0.40/0.52 (((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))))) <=> ((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | ((~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15)))))),
% 0.40/0.52 inference(monotonicity,[status(thm)],[150])).
% 0.40/0.52 tff(152,plain,
% 0.40/0.52 (((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))))) <=> ((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))))),
% 0.40/0.53 inference(transitivity,[status(thm)],[151, 149])).
% 0.40/0.53 tff(153,plain,
% 0.40/0.53 ((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))))),
% 0.40/0.53 inference(quant_inst,[status(thm)],[])).
% 0.40/0.53 tff(154,plain,
% 0.40/0.53 ((~![A: ty, L1: uni, L2: uni, K1: uni, K2: uni] : (permut(A, infix_plpl(A, L1, L2), infix_plpl(A, K1, K2)) | (~permut(A, L2, K2)) | (~permut(A, L1, K1)))) | (~permut(elt1, prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13)), t2tb(S2!15))) | (~permut(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), t2tb(S1!14))) | permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15)))),
% 0.40/0.53 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.40/0.53 tff(155,plain,
% 0.40/0.53 (permut(elt1, infix_plpl(elt1, prefix(elt1, div(N!12, 2), t2tb(L!11)), prefix(elt1, $sum(N!12, $product(-1, div(N!12, 2))), t2tb(L2!13))), infix_plpl(elt1, t2tb(S1!14), t2tb(S2!15)))),
% 0.40/0.53 inference(unit_resolution,[status(thm)],[154, 148, 138, 133])).
% 0.40/0.53 tff(156,plain,
% 0.40/0.53 ($false),
% 0.40/0.53 inference(unit_resolution,[status(thm)],[155, 128])).
% 0.40/0.53 % SZS output end Proof
%------------------------------------------------------------------------------