TSTP Solution File: SWW629_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW629_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 20:59:30 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW629_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 20:53:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(permut_type, type, (
% 0.19/0.46 permut: ( ty * uni * uni ) > $o)).
% 0.19/0.46 tff(infix_plpl_type, type, (
% 0.19/0.46 infix_plpl: ( ty * uni * uni ) > uni)).
% 0.19/0.46 tff(t2tb_type, type, (
% 0.19/0.46 t2tb: list_elt > uni)).
% 0.19/0.46 tff(tptp_fun_Q22_18_type, type, (
% 0.19/0.46 tptp_fun_Q22_18: list_elt)).
% 0.19/0.46 tff(tptp_fun_Q12_17_type, type, (
% 0.19/0.46 tptp_fun_Q12_17: list_elt)).
% 0.19/0.46 tff(elt_type, type, (
% 0.19/0.46 elt: ty)).
% 0.19/0.46 tff(tptp_fun_Q21_15_type, type, (
% 0.19/0.46 tptp_fun_Q21_15: list_elt)).
% 0.19/0.46 tff(tptp_fun_Q11_14_type, type, (
% 0.19/0.46 tptp_fun_Q11_14: list_elt)).
% 0.19/0.46 tff(tptp_fun_Q4_19_type, type, (
% 0.19/0.46 tptp_fun_Q4_19: list_elt)).
% 0.19/0.46 tff(tptp_fun_Q_10_type, type, (
% 0.19/0.46 tptp_fun_Q_10: list_elt)).
% 0.19/0.46 tff(sorted1_type, type, (
% 0.19/0.46 sorted1: list_elt > $o)).
% 0.19/0.46 tff(tb2t_type, type, (
% 0.19/0.46 tb2t: uni > list_elt)).
% 0.19/0.46 tff(nil_type, type, (
% 0.19/0.46 nil: ty > uni)).
% 0.19/0.46 tff(tptp_fun_Q3_13_type, type, (
% 0.19/0.46 tptp_fun_Q3_13: list_elt)).
% 0.19/0.46 tff(true1_type, type, (
% 0.19/0.46 true1: bool1)).
% 0.19/0.46 tff(tptp_fun_O_16_type, type, (
% 0.19/0.46 tptp_fun_O_16: bool1)).
% 0.19/0.46 tff(length2_type, type, (
% 0.19/0.46 length2: ( ty * uni ) > $int)).
% 0.19/0.46 tff(tptp_fun_Q2_12_type, type, (
% 0.19/0.46 tptp_fun_Q2_12: list_elt)).
% 0.19/0.46 tff(tptp_fun_Q1_11_type, type, (
% 0.19/0.46 tptp_fun_Q1_11: list_elt)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & ((Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) <=> ((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & (Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (((Q1!11 = tb2t(nil(elt))) & ((Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) <=> ((Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (((Q2!12 = tb2t(nil(elt))) & (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) <=> ((Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (((permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))) & ((O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) <=> (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (((O!16 = true1) & (sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)) & (Q3!13 = tb2t(nil(elt)))) <=> ((O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 ((~(~(Q3!13 = tb2t(nil(elt))))) <=> (Q3!13 = tb2t(nil(elt)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(7,plain,
% 0.19/0.47 ((~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) <=> permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (((sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))) <=> (sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 (((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & ((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)) & (sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))) <=> ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 ((~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))) <=> (sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(11,plain,
% 0.19/0.47 ((~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) <=> ((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 (((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))))) <=> ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & ((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)) & (sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[11, 10])).
% 0.19/0.47 tff(13,plain,
% 0.19/0.47 (((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))))) <=> ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[12, 9])).
% 0.19/0.47 tff(14,plain,
% 0.19/0.47 ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) <=> (sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(15,plain,
% 0.19/0.47 (((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) <=> ((sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[14, 13])).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 (((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) <=> (sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[15, 8])).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 ((~(~(O!16 = true1))) <=> (O!16 = true1)),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt)))))) <=> ((O!16 = true1) & (sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)) & (Q3!13 = tb2t(nil(elt))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[17, 16, 7, 6])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 (((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt)))))) <=> ((O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[18, 5])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) <=> (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 (((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt))))))) <=> ((permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))) & ((O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[20, 19])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt))))))) <=> (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[21, 4])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 ((~(~(Q2!12 = tb2t(nil(elt))))) <=> (Q2!12 = tb2t(nil(elt)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (((~(~(Q2!12 = tb2t(nil(elt))))) & ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt)))))))) <=> ((Q2!12 = tb2t(nil(elt))) & (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[23, 22])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (((~(~(Q2!12 = tb2t(nil(elt))))) & ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt)))))))) <=> ((Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[24, 3])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 ((~(~(Q1!11 = tb2t(nil(elt))))) <=> (Q1!11 = tb2t(nil(elt)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(27,plain,
% 0.19/0.48 (((~(~(Q1!11 = tb2t(nil(elt))))) & ((~(~(Q2!12 = tb2t(nil(elt))))) & ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt))))))))) <=> ((Q1!11 = tb2t(nil(elt))) & ((Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[26, 25])).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (((~(~(Q1!11 = tb2t(nil(elt))))) & ((~(~(Q2!12 = tb2t(nil(elt))))) & ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt))))))))) <=> ((Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[27, 2])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 (((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & ((~(~(Q1!11 = tb2t(nil(elt))))) & ((~(~(Q2!12 = tb2t(nil(elt))))) & ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt)))))))))) <=> ((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & ((Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 (((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & ((~(~(Q1!11 = tb2t(nil(elt))))) & ((~(~(Q2!12 = tb2t(nil(elt))))) & ((~(~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1)))))) & ((~(~(O!16 = true1))) & ((~(~(sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14))))) & ((~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (~(~((Q3!13 = tb2t(nil(elt))) & sorted1(Q12!17) & sorted1(Q22!18)))) & (~(~(sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15))))))) & (~(~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))) & (~(~(Q3!13 = tb2t(nil(elt)))))))))) <=> ((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & (Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[29, 1])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 ((~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = -1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))) <=> (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = -1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 ((~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q11)), $product(-1, length2(elt, t2tb(Q21)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q11)), $product(-1, length2(elt, t2tb(Q21)))) = 1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))) <=> (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = -1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 ((~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))) <=> (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q11)), $product(-1, length2(elt, t2tb(Q21)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q11)), $product(-1, length2(elt, t2tb(Q21)))) = 1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 ((~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt)))))))))) <=> (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(35,plain,
% 0.19/0.49 ((~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt)))))))))) <=> (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 ((~![Q: list_elt] : ($less(1, length2(elt, t2tb(Q))) => ![Q1: list_elt] : ((Q1 = tb2t(nil(elt))) => ![Q2: list_elt] : ((Q2 = tb2t(nil(elt))) => ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(length2(elt, t2tb(Q21)), 1))))) => ![O: bool1] : (((O = true1) <=> (Q3 = tb2t(nil(elt)))) => ((~(~(O = true1))) => ((Q3 = tb2t(nil(elt))) => (permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q)) => ![Q12: list_elt] : ((sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11))) => ![Q22: list_elt] : ((sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21))) => ((((Q3 = tb2t(nil(elt))) & sorted1(Q12)) & sorted1(Q22)) => ![Q4: list_elt] : ((sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22)))) => (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))))))))))))))) <=> (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt))))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(37,axiom,(~![Q: list_elt] : ($less(1, length2(elt, t2tb(Q))) => ![Q1: list_elt] : ((Q1 = tb2t(nil(elt))) => ![Q2: list_elt] : ((Q2 = tb2t(nil(elt))) => ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(length2(elt, t2tb(Q21)), 1))))) => ![O: bool1] : (((O = true1) <=> (Q3 = tb2t(nil(elt)))) => ((~(~(O = true1))) => ((Q3 = tb2t(nil(elt))) => (permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q)) => ![Q12: list_elt] : ((sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11))) => ![Q22: list_elt] : ((sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21))) => ((((Q3 = tb2t(nil(elt))) & sorted1(Q12)) & sorted1(Q22)) => ![Q4: list_elt] : ((sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22)))) => (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_mergesort')).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))) | ((~(O = true1)) <=> (Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & ((length2(elt, t2tb(Q11)) = length2(elt, t2tb(Q21))) | ((length2(elt, t2tb(Q3)) = 0) & (length2(elt, t2tb(Q11)) = $sum(1, length2(elt, t2tb(Q21)))))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q11)), $product(-1, length2(elt, t2tb(Q21)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q11)), $product(-1, length2(elt, t2tb(Q21)))) = 1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = -1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = -1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[43, 31])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (~![Q: list_elt] : ($lesseq(length2(elt, t2tb(Q)), 1) | ![Q1: list_elt] : ((~(Q1 = tb2t(nil(elt)))) | ![Q2: list_elt] : ((~(Q2 = tb2t(nil(elt)))) | ![Q21: list_elt, Q11: list_elt, Q3: list_elt] : ((~(permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q3)), t2tb(Q)) & (($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = 0) | ((length2(elt, t2tb(Q3)) = 0) & ($sum(length2(elt, t2tb(Q21)), $product(-1, length2(elt, t2tb(Q11)))) = -1))))) | ![O: bool1] : ((~(O = true1)) | ![Q12: list_elt] : ((~(sorted1(Q12) & permut(elt, t2tb(Q12), t2tb(Q11)))) | ![Q22: list_elt] : (![Q4: list_elt] : ((~(sorted1(Q4) & permut(elt, t2tb(Q4), infix_plpl(elt, t2tb(Q12), t2tb(Q22))))) | (sorted1(Q4) & permut(elt, t2tb(Q4), t2tb(Q)))) | (~((Q3 = tb2t(nil(elt))) & sorted1(Q12) & sorted1(Q22))) | (~(sorted1(Q22) & permut(elt, t2tb(Q22), t2tb(Q21)))))) | (~permut(elt, infix_plpl(elt, t2tb(Q11), t2tb(Q21)), t2tb(Q))) | (~(Q3 = tb2t(nil(elt)))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 ((~$lesseq(length2(elt, t2tb(Q!10)), 1)) & (Q1!11 = tb2t(nil(elt))) & (Q2!12 = tb2t(nil(elt))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q3!13)), t2tb(Q!10)) & (($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = 0) | ((length2(elt, t2tb(Q3!13)) = 0) & ($sum(length2(elt, t2tb(Q21!15)), $product(-1, length2(elt, t2tb(Q11!14)))) = -1))) & (O!16 = true1) & sorted1(Q12!17) & permut(elt, t2tb(Q12!17), t2tb(Q11!14)) & (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))) & (Q3!13 = tb2t(nil(elt))) & sorted1(Q22!18) & permut(elt, t2tb(Q22!18), t2tb(Q21!15)) & permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[45, 30])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))),
% 0.19/0.49 inference(and_elim,[status(thm)],[46])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (~((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) | (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))))),
% 0.19/0.49 inference(and_elim,[status(thm)],[46])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (sorted1(Q4!19) & permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))),
% 0.19/0.49 inference(or_elim,[status(thm)],[48])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 (sorted1(Q4!19)),
% 0.19/0.49 inference(and_elim,[status(thm)],[49])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 ((~(~((~sorted1(Q4!19)) | (~permut(elt, t2tb(Q4!19), t2tb(Q!10)))))) <=> ((~sorted1(Q4!19)) | (~permut(elt, t2tb(Q4!19), t2tb(Q!10))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 ((sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10))) <=> (~((~sorted1(Q4!19)) | (~permut(elt, t2tb(Q4!19), t2tb(Q!10)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 ((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10)))) <=> (~(~((~sorted1(Q4!19)) | (~permut(elt, t2tb(Q4!19), t2tb(Q!10))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 ((~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10)))) <=> ((~sorted1(Q4!19)) | (~permut(elt, t2tb(Q4!19), t2tb(Q!10))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[53, 51])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (~(sorted1(Q4!19) & permut(elt, t2tb(Q4!19), t2tb(Q!10)))),
% 0.19/0.49 inference(or_elim,[status(thm)],[48])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 ((~sorted1(Q4!19)) | (~permut(elt, t2tb(Q4!19), t2tb(Q!10)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (~permut(elt, t2tb(Q4!19), t2tb(Q!10))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[56, 50])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.49 tff(63,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')).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.49 tff(66,plain,(
% 0.19/0.49 ![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[65])).
% 0.19/0.49 tff(67,plain,
% 0.19/0.49 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | ((~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(69,plain,
% 0.19/0.49 ((permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15))))) <=> ((~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | ((~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q!10))) | permut(elt, t2tb(Q4!19), t2tb(Q!10)) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[73, 67, 57, 47])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (^[A: ty, L1: uni, L2: uni] : refl(((~permut(A, L1, L2)) | permut(A, L2, L1)) <=> ((~permut(A, L1, L2)) | permut(A, L2, L1)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 (![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))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 (![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))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(78,plain,
% 0.19/0.50 (^[A: ty, L1: uni, L2: uni] : rewrite((permut(A, L1, L2) => permut(A, L2, L1)) <=> ((~permut(A, L1, L2)) | permut(A, L2, L1)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (![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))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.50 tff(80,axiom,(![A: ty, L1: uni, L2: uni] : (permut(A, L1, L2) => permut(A, L2, L1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_sym')).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.50 tff(83,plain,(
% 0.19/0.50 ![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.19/0.50 inference(skolemize,[status(sab)],[82])).
% 0.19/0.50 tff(84,plain,
% 0.19/0.50 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.50 tff(85,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19))) | permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15))))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19))) | permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(86,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19))) | permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(87,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19))) | permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.50 tff(88,plain,
% 0.19/0.50 (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[87, 84, 74])).
% 0.19/0.50 tff(89,plain,
% 0.19/0.50 (permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[49])).
% 0.19/0.50 tff(90,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))) | permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19)))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))) | permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(91,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))) | permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(92,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, t2tb(Q4!19), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))) | permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.50 tff(93,plain,
% 0.19/0.50 (permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[92, 84, 89])).
% 0.19/0.50 tff(94,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | ((~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(95,plain,
% 0.19/0.50 ((permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) <=> ((~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(96,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | ((~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.50 tff(97,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))) <=> ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.50 tff(98,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(99,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))) | (~permut(elt, infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)), t2tb(Q4!19))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), t2tb(Q4!19)) | (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.50 tff(100,plain,
% 0.19/0.50 (~permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[99, 67, 93, 88])).
% 0.19/0.50 tff(101,plain,
% 0.19/0.50 (permut(elt, t2tb(Q22!18), t2tb(Q21!15))),
% 0.19/0.50 inference(and_elim,[status(thm)],[46])).
% 0.19/0.50 tff(102,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, t2tb(Q22!18), t2tb(Q21!15))) | permut(elt, t2tb(Q21!15), t2tb(Q22!18)))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, t2tb(Q22!18), t2tb(Q21!15))) | permut(elt, t2tb(Q21!15), t2tb(Q22!18)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(103,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, t2tb(Q22!18), t2tb(Q21!15))) | permut(elt, t2tb(Q21!15), t2tb(Q22!18)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(104,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, t2tb(Q22!18), t2tb(Q21!15))) | permut(elt, t2tb(Q21!15), t2tb(Q22!18))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.50 tff(105,plain,
% 0.19/0.50 (permut(elt, t2tb(Q21!15), t2tb(Q22!18))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[104, 84, 101])).
% 0.19/0.50 tff(106,plain,
% 0.19/0.50 (permut(elt, t2tb(Q12!17), t2tb(Q11!14))),
% 0.19/0.50 inference(and_elim,[status(thm)],[46])).
% 0.19/0.50 tff(107,plain,
% 0.19/0.50 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, t2tb(Q12!17), t2tb(Q11!14))) | permut(elt, t2tb(Q11!14), t2tb(Q12!17)))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, t2tb(Q12!17), t2tb(Q11!14))) | permut(elt, t2tb(Q11!14), t2tb(Q12!17)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(108,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, t2tb(Q12!17), t2tb(Q11!14))) | permut(elt, t2tb(Q11!14), t2tb(Q12!17)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(109,plain,
% 0.19/0.50 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, t2tb(Q12!17), t2tb(Q11!14))) | permut(elt, t2tb(Q11!14), t2tb(Q12!17))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.50 tff(110,plain,
% 0.19/0.50 (permut(elt, t2tb(Q11!14), t2tb(Q12!17))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[109, 84, 106])).
% 0.19/0.50 tff(111,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(112,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.50 tff(113,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(114,plain,
% 0.19/0.50 (^[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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.50 tff(116,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')).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.19/0.50 tff(119,plain,(
% 0.19/0.50 ![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)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[118])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 (((~![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(elt, t2tb(Q11!14), t2tb(Q12!17))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))) <=> ((~![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(elt, t2tb(Q11!14), t2tb(Q12!17))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 ((permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | (~permut(elt, t2tb(Q11!14), t2tb(Q12!17)))) <=> ((~permut(elt, t2tb(Q11!14), t2tb(Q12!17))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 (((~![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(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | (~permut(elt, t2tb(Q11!14), t2tb(Q12!17))))) <=> ((~![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(elt, t2tb(Q11!14), t2tb(Q12!17))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (((~![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(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | (~permut(elt, t2tb(Q11!14), t2tb(Q12!17))))) <=> ((~![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(elt, t2tb(Q11!14), t2tb(Q12!17))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[123, 121])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 ((~![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(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | (~permut(elt, t2tb(Q11!14), t2tb(Q12!17))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 ((~![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(elt, t2tb(Q11!14), t2tb(Q12!17))) | (~permut(elt, t2tb(Q21!15), t2tb(Q22!18))) | permut(elt, infix_plpl(elt, t2tb(Q11!14), t2tb(Q21!15)), infix_plpl(elt, t2tb(Q12!17), t2tb(Q22!18)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[126, 120, 110, 105, 100])).
% 0.19/0.51 % SZS output end Proof
%------------------------------------------------------------------------------