TSTP Solution File: SWW628_2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW628_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.61s 0.66s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW628_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 : n020.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 20:28:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.61/0.66 % SZS status Theorem
% 0.61/0.66 % SZS output start Proof
% 0.61/0.66 tff(permut_type, type, (
% 0.61/0.66 permut: ( ty * uni * uni ) > $o)).
% 0.61/0.66 tff(infix_plpl_type, type, (
% 0.61/0.66 infix_plpl: ( ty * uni * uni ) > uni)).
% 0.61/0.66 tff(t2tb_type, type, (
% 0.61/0.66 t2tb: list_elt > uni)).
% 0.61/0.66 tff(tptp_fun_X3_20_type, type, (
% 0.61/0.66 tptp_fun_X3_20: list_elt)).
% 0.61/0.66 tff(cons_type, type, (
% 0.61/0.66 cons: ( ty * uni * uni ) > uni)).
% 0.61/0.66 tff(tptp_fun_X2_25_type, type, (
% 0.61/0.66 tptp_fun_X2_25: list_elt)).
% 0.61/0.66 tff(t2tb1_type, type, (
% 0.61/0.66 t2tb1: elt1 > uni)).
% 0.61/0.66 tff(tptp_fun_X_26_type, type, (
% 0.61/0.66 tptp_fun_X_26: elt1)).
% 0.61/0.66 tff(elt_type, type, (
% 0.61/0.66 elt: ty)).
% 0.61/0.66 tff(nil_type, type, (
% 0.61/0.66 nil: ty > uni)).
% 0.61/0.66 tff(tptp_fun_O_18_type, type, (
% 0.61/0.66 tptp_fun_O_18: elt1)).
% 0.61/0.66 tff(tptp_fun_Q21_14_type, type, (
% 0.61/0.66 tptp_fun_Q21_14: list_elt)).
% 0.61/0.66 tff(tptp_fun_Q11_13_type, type, (
% 0.61/0.66 tptp_fun_Q11_13: list_elt)).
% 0.61/0.66 tff(tptp_fun_X_21_type, type, (
% 0.61/0.66 tptp_fun_X_21: elt1)).
% 0.61/0.66 tff(reverse_type, type, (
% 0.61/0.66 reverse: ( ty * uni ) > uni)).
% 0.61/0.66 tff(tptp_fun_Q2_11_type, type, (
% 0.61/0.66 tptp_fun_Q2_11: list_elt)).
% 0.61/0.66 tff(tptp_fun_Q1_12_type, type, (
% 0.61/0.66 tptp_fun_Q1_12: list_elt)).
% 0.61/0.66 tff(tptp_fun_Q3_15_type, type, (
% 0.61/0.66 tptp_fun_Q3_15: list_elt)).
% 0.61/0.66 tff(mem_type, type, (
% 0.61/0.66 mem: ( ty * uni * uni ) > $o)).
% 0.61/0.66 tff(le1_type, type, (
% 0.61/0.66 le1: ( elt1 * elt1 ) > $o)).
% 0.61/0.66 tff(sorted1_type, type, (
% 0.61/0.66 sorted1: list_elt > $o)).
% 0.61/0.66 tff(tptp_fun_X1_16_type, type, (
% 0.61/0.66 tptp_fun_X1_16: elt1)).
% 0.61/0.66 tff(tb2t_type, type, (
% 0.61/0.66 tb2t: uni > list_elt)).
% 0.61/0.66 tff(tptp_fun_X_24_type, type, (
% 0.61/0.66 tptp_fun_X_24: elt1)).
% 0.61/0.66 tff(tptp_fun_X2_17_type, type, (
% 0.61/0.66 tptp_fun_X2_17: elt1)).
% 0.61/0.66 tff(tptp_fun_X3_23_type, type, (
% 0.61/0.66 tptp_fun_X3_23: list_elt)).
% 0.61/0.66 tff(tptp_fun_Q22_19_type, type, (
% 0.61/0.66 tptp_fun_Q22_19: list_elt)).
% 0.61/0.66 tff(tptp_fun_Q4_22_type, type, (
% 0.61/0.66 tptp_fun_Q4_22: list_elt)).
% 0.61/0.66 tff(length2_type, type, (
% 0.61/0.66 length2: ( ty * uni ) > $int)).
% 0.61/0.66 tff(tptp_fun_Q_10_type, type, (
% 0.61/0.66 tptp_fun_Q_10: list_elt)).
% 0.61/0.66 tff(1,plain,
% 0.61/0.66 (^[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)))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(2,plain,
% 0.61/0.66 (![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))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[1])).
% 0.61/0.66 tff(3,plain,
% 0.61/0.66 (^[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)))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(4,plain,
% 0.61/0.66 (![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))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[3])).
% 0.61/0.66 tff(5,plain,
% 0.61/0.66 (![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))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[4, 2])).
% 0.61/0.66 tff(6,plain,
% 0.61/0.66 (^[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)))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(7,plain,
% 0.61/0.66 (![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))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[6])).
% 0.61/0.66 tff(8,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 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/sandbox2/benchmark/theBenchmark.p','infix_plpl_def')).
% 0.61/0.66 tff(10,plain,
% 0.61/0.66 (![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))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.61/0.66 tff(11,plain,(
% 0.61/0.66 ![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))))),
% 0.61/0.66 inference(skolemize,[status(sab)],[10])).
% 0.61/0.66 tff(12,plain,
% 0.61/0.66 (![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))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.61/0.66 tff(13,plain,
% 0.61/0.66 (![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))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.61/0.66 tff(14,plain,
% 0.61/0.66 ((~![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(elt, nil(elt), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, t2tb1(O!18), nil(elt)))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, X, infix_plpl(elt, X1, cons(elt, t2tb1(O!18), nil(elt))))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(15,plain,
% 0.61/0.66 (~((~(infix_plpl(elt, nil(elt), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, t2tb1(O!18), nil(elt)))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, X, infix_plpl(elt, X1, cons(elt, t2tb1(O!18), nil(elt)))))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.61/0.66 tff(16,plain,
% 0.61/0.66 (((~(infix_plpl(elt, nil(elt), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, t2tb1(O!18), nil(elt)))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, X, infix_plpl(elt, X1, cons(elt, t2tb1(O!18), nil(elt))))))) | (infix_plpl(elt, nil(elt), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, t2tb1(O!18), nil(elt)))),
% 0.61/0.66 inference(tautology,[status(thm)],[])).
% 0.61/0.66 tff(17,plain,
% 0.61/0.66 (infix_plpl(elt, nil(elt), cons(elt, t2tb1(O!18), nil(elt))) = cons(elt, t2tb1(O!18), nil(elt))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.61/0.66 tff(18,plain,
% 0.61/0.66 ((((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11)) & ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) <=> ((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11) & (~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(19,plain,
% 0.61/0.66 (((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & ((~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26)) & (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) <=> ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(20,plain,
% 0.61/0.66 ((sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))) <=> (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(21,plain,
% 0.61/0.67 (((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24)) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) <=> ((~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(22,plain,
% 0.61/0.67 (((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) <=> ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(23,plain,
% 0.61/0.67 ((((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) <=> ((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))))),
% 0.61/0.67 inference(rewrite,[status(thm)],[])).
% 0.61/0.67 tff(24,plain,
% 0.61/0.67 (((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) <=> ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24)))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[23])).
% 0.61/0.67 tff(25,plain,
% 0.61/0.67 (((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) <=> ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))),
% 0.61/0.67 inference(transitivity,[status(thm)],[24, 22])).
% 0.61/0.67 tff(26,plain,
% 0.61/0.67 (((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) <=> ((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24)) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26)))),
% 0.61/0.67 inference(monotonicity,[status(thm)],[25])).
% 0.61/0.67 tff(27,plain,
% 0.61/0.67 (((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) <=> ((~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))),
% 0.61/0.67 inference(transitivity,[status(thm)],[26, 21])).
% 0.61/0.67 tff(28,plain,
% 0.61/0.67 (((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & ((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) & (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) <=> ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & ((~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26)) & (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[27, 20])).
% 0.61/0.68 tff(29,plain,
% 0.61/0.68 (((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & ((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) & (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) <=> ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))),
% 0.61/0.68 inference(transitivity,[status(thm)],[28, 19])).
% 0.61/0.68 tff(30,plain,
% 0.61/0.68 ((~(~((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11)))) <=> ((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(31,plain,
% 0.61/0.68 (((~(~((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11)))) & ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & ((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) & (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) <=> (((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11)) & ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))),
% 0.61/0.68 inference(monotonicity,[status(thm)],[30, 29])).
% 0.61/0.68 tff(32,plain,
% 0.61/0.68 (((~(~((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11)))) & ((~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & ((~(Q21!14 = tb2t(nil(elt)))) & ((~le1(X1!16, X2!17)) & (~(Q21!14 = tb2t(nil(elt)))) & (((Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20)) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) & ((Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24))) & ((Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26))) & (sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))))) <=> ((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11) & (~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))),
% 0.61/0.68 inference(transitivity,[status(thm)],[31, 18])).
% 0.61/0.68 tff(33,plain,
% 0.61/0.68 ((~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))) <=> (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(34,plain,
% 0.61/0.68 ((~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((((Q = tb2t(nil(elt))) & sorted1(Q1)) & sorted1(Q2)) => ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((((((sorted1(Q11) & sorted1(Q21)) & sorted1(Q3)) & ![X: elt1, Y: elt1] : (mem(elt, t2tb1(X), t2tb(Q3)) => (mem(elt, t2tb1(Y), t2tb(Q11)) => le1(X, Y)))) & ![X: elt1, Y: elt1] : (mem(elt, t2tb1(X), t2tb(Q3)) => (mem(elt, t2tb1(Y), t2tb(Q21)) => le1(X, Y)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))) => ($less(0, length2(elt, t2tb(Q11))) => ((~(length2(elt, t2tb(Q11)) = 0)) => ((~(length2(elt, t2tb(Q21)) = 0)) => ((~(Q11 = tb2t(nil(elt)))) => ![X1: elt1] : (?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)) => ((~(Q21 = tb2t(nil(elt)))) => ![X2: elt1] : (?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)) => ((~le1(X1, X2)) => ((~(Q21 = tb2t(nil(elt)))) => ![Q22: list_elt, O: elt1] : (?[X: elt1, X3: list_elt] : (((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X)) & (Q22 = X3)) => ![Q4: list_elt] : ((Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt))))) => permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))))))))))))))) <=> (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))))))),
% 0.61/0.68 inference(rewrite,[status(thm)],[])).
% 0.61/0.68 tff(35,axiom,(~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((((Q = tb2t(nil(elt))) & sorted1(Q1)) & sorted1(Q2)) => ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((((((sorted1(Q11) & sorted1(Q21)) & sorted1(Q3)) & ![X: elt1, Y: elt1] : (mem(elt, t2tb1(X), t2tb(Q3)) => (mem(elt, t2tb1(Y), t2tb(Q11)) => le1(X, Y)))) & ![X: elt1, Y: elt1] : (mem(elt, t2tb1(X), t2tb(Q3)) => (mem(elt, t2tb1(Y), t2tb(Q21)) => le1(X, Y)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))) => ($less(0, length2(elt, t2tb(Q11))) => ((~(length2(elt, t2tb(Q11)) = 0)) => ((~(length2(elt, t2tb(Q21)) = 0)) => ((~(Q11 = tb2t(nil(elt)))) => ![X1: elt1] : (?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)) => ((~(Q21 = tb2t(nil(elt)))) => ![X2: elt1] : (?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)) => ((~le1(X1, X2)) => ((~(Q21 = tb2t(nil(elt)))) => ![Q22: list_elt, O: elt1] : (?[X: elt1, X3: list_elt] : (((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X)) & (Q22 = X3)) => ![Q4: list_elt] : ((Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt))))) => permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wP_parameter_merge')).
% 0.61/0.68 tff(36,plain,
% 0.61/0.68 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.61/0.68 tff(37,plain,
% 0.61/0.68 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.61/0.68 tff(38,plain,
% 0.61/0.68 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.68 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.61/0.68 tff(39,plain,
% 0.61/0.68 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.61/0.69 tff(40,plain,
% 0.61/0.69 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.61/0.69 tff(41,plain,
% 0.61/0.69 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.61/0.69 tff(42,plain,
% 0.61/0.69 (~![Q1: list_elt, Q2: list_elt, Q: list_elt] : ((~((Q = tb2t(nil(elt))) & sorted1(Q1) & sorted1(Q2))) | ![Q3: list_elt, Q21: list_elt, Q11: list_elt] : ((Q11 = tb2t(nil(elt))) | (length2(elt, t2tb(Q21)) = 0) | (length2(elt, t2tb(Q11)) = 0) | $lesseq(length2(elt, t2tb(Q11)), 0) | ![X1: elt1] : ((Q21 = tb2t(nil(elt))) | ![X2: elt1] : (le1(X1, X2) | (Q21 = tb2t(nil(elt))) | ![Q22: list_elt, O: elt1] : ((~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (O = X) & (Q22 = X3))) | ![Q4: list_elt] : ((~(Q4 = tb2t(infix_plpl(elt, t2tb(Q3), cons(elt, t2tb1(O), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4), t2tb(Q11)), t2tb(Q22)), infix_plpl(elt, t2tb(Q1), t2tb(Q2))))) | (~?[X: elt1, X3: list_elt] : ((Q21 = tb2t(cons(elt, t2tb1(X), t2tb(X3)))) & (X2 = X)))) | (~?[X: elt1, X2: list_elt] : ((Q11 = tb2t(cons(elt, t2tb1(X), t2tb(X2)))) & (X1 = X)))) | (~(sorted1(Q11) & sorted1(Q21) & sorted1(Q3) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11))) | (~mem(elt, t2tb1(X), t2tb(Q3)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3))) | (~mem(elt, t2tb1(Y), t2tb(Q21)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3), t2tb(Q11)), t2tb(Q21)), infix_plpl(elt, t2tb(Q1), t2tb(Q2)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.61/0.69 tff(43,plain,
% 0.61/0.69 ((Q!10 = tb2t(nil(elt))) & sorted1(Q1!12) & sorted1(Q2!11) & (~(Q11!13 = tb2t(nil(elt)))) & (~(length2(elt, t2tb(Q21!14)) = 0)) & (~(length2(elt, t2tb(Q11!13)) = 0)) & (~$lesseq(length2(elt, t2tb(Q11!13)), 0)) & (~(Q21!14 = tb2t(nil(elt)))) & (~le1(X1!16, X2!17)) & (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) & (O!18 = X!21) & (Q22!19 = X3!20) & (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))) & (Q21!14 = tb2t(cons(elt, t2tb1(X!24), t2tb(X3!23)))) & (X2!17 = X!24) & (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) & (X1!16 = X!26) & sorted1(Q11!13) & sorted1(Q21!14) & sorted1(Q3!15) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(Y), t2tb(Q11!13))) | (~mem(elt, t2tb1(X), t2tb(Q3!15)))) & ![X: elt1, Y: elt1] : (le1(X, Y) | (~mem(elt, t2tb1(X), t2tb(Q3!15))) | (~mem(elt, t2tb1(Y), t2tb(Q21!14)))) & permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.61/0.69 tff(44,plain,
% 0.61/0.69 (O!18 = X!21),
% 0.61/0.69 inference(and_elim,[status(thm)],[43])).
% 0.61/0.69 tff(45,plain,
% 0.61/0.69 (t2tb1(O!18) = t2tb1(X!21)),
% 0.61/0.69 inference(monotonicity,[status(thm)],[44])).
% 0.61/0.69 tff(46,plain,
% 0.61/0.69 (t2tb1(X!21) = t2tb1(O!18)),
% 0.61/0.69 inference(symmetry,[status(thm)],[45])).
% 0.61/0.69 tff(47,plain,
% 0.61/0.69 (cons(elt, t2tb1(X!21), nil(elt)) = cons(elt, t2tb1(O!18), nil(elt))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[46])).
% 0.61/0.69 tff(48,plain,
% 0.61/0.69 (^[A: ty] : refl((~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))) <=> (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))))),
% 0.61/0.69 inference(bind,[status(th)],[])).
% 0.61/0.69 tff(49,plain,
% 0.61/0.69 (![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))) <=> ![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))),
% 0.61/0.69 inference(quant_intro,[status(thm)],[48])).
% 0.61/0.69 tff(50,plain,
% 0.61/0.69 (^[A: ty] : rewrite((~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))) <=> (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))))),
% 0.61/0.69 inference(bind,[status(th)],[])).
% 0.61/0.69 tff(51,plain,
% 0.61/0.69 (![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))) <=> ![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))),
% 0.61/0.69 inference(quant_intro,[status(thm)],[50])).
% 0.61/0.69 tff(52,plain,
% 0.61/0.69 (![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))) <=> ![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))),
% 0.61/0.69 inference(transitivity,[status(thm)],[51, 49])).
% 0.61/0.69 tff(53,plain,
% 0.61/0.69 (^[A: ty] : rewrite(((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))) <=> (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))))))),
% 0.61/0.69 inference(bind,[status(th)],[])).
% 0.61/0.69 tff(54,plain,
% 0.61/0.69 (![A: ty] : ((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))) <=> ![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))),
% 0.61/0.69 inference(quant_intro,[status(thm)],[53])).
% 0.61/0.69 tff(55,plain,
% 0.61/0.69 (![A: ty] : ((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A))))) <=> ![A: ty] : ((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(56,axiom,(![A: ty] : ((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reverse_def')).
% 0.61/0.69 tff(57,plain,
% 0.61/0.69 (![A: ty] : ((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.61/0.69 tff(58,plain,(
% 0.61/0.69 ![A: ty] : ((reverse(A, nil(A)) = nil(A)) & ![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))),
% 0.61/0.69 inference(skolemize,[status(sab)],[57])).
% 0.61/0.69 tff(59,plain,
% 0.61/0.69 (![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.61/0.69 tff(60,plain,
% 0.61/0.69 (![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.61/0.69 tff(61,plain,
% 0.61/0.69 ((~![A: ty] : (~((~(reverse(A, nil(A)) = nil(A))) | (~![X: uni, X1: uni] : (reverse(A, cons(A, X, X1)) = infix_plpl(A, reverse(A, X1), cons(A, X, nil(A)))))))) | (~((~(reverse(elt, nil(elt)) = nil(elt))) | (~![X: uni, X1: uni] : (reverse(elt, cons(elt, X, X1)) = infix_plpl(elt, reverse(elt, X1), cons(elt, X, nil(elt)))))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(62,plain,
% 0.61/0.69 (~((~(reverse(elt, nil(elt)) = nil(elt))) | (~![X: uni, X1: uni] : (reverse(elt, cons(elt, X, X1)) = infix_plpl(elt, reverse(elt, X1), cons(elt, X, nil(elt))))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.61/0.69 tff(63,plain,
% 0.61/0.69 (((~(reverse(elt, nil(elt)) = nil(elt))) | (~![X: uni, X1: uni] : (reverse(elt, cons(elt, X, X1)) = infix_plpl(elt, reverse(elt, X1), cons(elt, X, nil(elt)))))) | (reverse(elt, nil(elt)) = nil(elt))),
% 0.61/0.69 inference(tautology,[status(thm)],[])).
% 0.61/0.69 tff(64,plain,
% 0.61/0.69 (reverse(elt, nil(elt)) = nil(elt)),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.61/0.69 tff(65,plain,
% 0.61/0.69 (infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), nil(elt))) = infix_plpl(elt, nil(elt), cons(elt, t2tb1(O!18), nil(elt)))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[64, 47])).
% 0.61/0.69 tff(66,plain,
% 0.61/0.69 (^[A: ty, L: uni, X: uni] : refl((reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A)))) <=> (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A)))))),
% 0.61/0.69 inference(bind,[status(th)],[])).
% 0.61/0.69 tff(67,plain,
% 0.61/0.69 (![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A)))) <=> ![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))),
% 0.61/0.69 inference(quant_intro,[status(thm)],[66])).
% 0.61/0.69 tff(68,plain,
% 0.61/0.69 (![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A)))) <=> ![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(69,axiom,(![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reverse_cons')).
% 0.61/0.69 tff(70,plain,
% 0.61/0.69 (![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.61/0.69 tff(71,plain,(
% 0.61/0.69 ![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))),
% 0.61/0.69 inference(skolemize,[status(sab)],[70])).
% 0.61/0.69 tff(72,plain,
% 0.61/0.69 (![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.61/0.69 tff(73,plain,
% 0.61/0.69 ((~![A: ty, L: uni, X: uni] : (reverse(A, cons(A, X, L)) = infix_plpl(A, reverse(A, L), cons(A, X, nil(A))))) | (reverse(elt, cons(elt, t2tb1(X!21), nil(elt))) = infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), nil(elt))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(74,plain,
% 0.61/0.69 (reverse(elt, cons(elt, t2tb1(X!21), nil(elt))) = infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), nil(elt)))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.61/0.69 tff(75,plain,
% 0.61/0.69 (reverse(elt, cons(elt, t2tb1(X!21), nil(elt))) = cons(elt, t2tb1(O!18), nil(elt))),
% 0.61/0.69 inference(transitivity,[status(thm)],[74, 65, 17])).
% 0.61/0.69 tff(76,plain,
% 0.61/0.69 (infix_plpl(elt, reverse(elt, cons(elt, t2tb1(X!21), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25))) = infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[75])).
% 0.61/0.69 tff(77,plain,
% 0.61/0.69 (^[A: ty, L1: uni, L2: uni, X: uni] : refl((infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2))) <=> (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2))))),
% 0.61/0.69 inference(bind,[status(th)],[])).
% 0.61/0.69 tff(78,plain,
% 0.61/0.69 (![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2))) <=> ![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))),
% 0.61/0.69 inference(quant_intro,[status(thm)],[77])).
% 0.61/0.69 tff(79,plain,
% 0.61/0.69 (![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2))) <=> ![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))),
% 0.61/0.69 inference(rewrite,[status(thm)],[])).
% 0.61/0.69 tff(80,axiom,(![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reverse_append')).
% 0.61/0.69 tff(81,plain,
% 0.61/0.69 (![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.61/0.69 tff(82,plain,(
% 0.61/0.69 ![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))),
% 0.61/0.69 inference(skolemize,[status(sab)],[81])).
% 0.61/0.69 tff(83,plain,
% 0.61/0.69 (![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))),
% 0.61/0.69 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.61/0.69 tff(84,plain,
% 0.61/0.69 ((~![A: ty, L1: uni, L2: uni, X: uni] : (infix_plpl(A, reverse(A, cons(A, X, L1)), L2) = infix_plpl(A, reverse(A, L1), cons(A, X, L2)))) | (infix_plpl(elt, reverse(elt, cons(elt, t2tb1(X!21), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25))) = infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))))),
% 0.61/0.69 inference(quant_inst,[status(thm)],[])).
% 0.61/0.69 tff(85,plain,
% 0.61/0.69 (infix_plpl(elt, reverse(elt, cons(elt, t2tb1(X!21), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25))) = infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.69 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.61/0.69 tff(86,plain,
% 0.61/0.69 (infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = infix_plpl(elt, reverse(elt, cons(elt, t2tb1(X!21), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.69 inference(symmetry,[status(thm)],[85])).
% 0.61/0.69 tff(87,plain,
% 0.61/0.69 (nil(elt) = reverse(elt, nil(elt))),
% 0.61/0.69 inference(symmetry,[status(thm)],[64])).
% 0.61/0.69 tff(88,plain,
% 0.61/0.69 (infix_plpl(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = infix_plpl(elt, reverse(elt, nil(elt)), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.69 inference(monotonicity,[status(thm)],[87])).
% 0.61/0.69 tff(89,plain,
% 0.61/0.69 ((~![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(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, X, infix_plpl(elt, X1, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))))))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(90,plain,
% 0.61/0.70 (~((~(infix_plpl(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, X, infix_plpl(elt, X1, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[89, 13])).
% 0.61/0.70 tff(91,plain,
% 0.61/0.70 (((~(infix_plpl(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, X, infix_plpl(elt, X1, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))))))) | (infix_plpl(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.70 inference(tautology,[status(thm)],[])).
% 0.61/0.70 tff(92,plain,
% 0.61/0.70 (infix_plpl(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.61/0.70 tff(93,plain,
% 0.61/0.70 (cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))) = infix_plpl(elt, nil(elt), cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.70 inference(symmetry,[status(thm)],[92])).
% 0.61/0.70 tff(94,plain,
% 0.61/0.70 (cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))) = infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.70 inference(transitivity,[status(thm)],[93, 88, 86, 76])).
% 0.61/0.70 tff(95,plain,
% 0.61/0.70 (infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)) = infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[94])).
% 0.61/0.70 tff(96,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))) <=> permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[95])).
% 0.61/0.70 tff(97,plain,
% 0.61/0.70 (Q21!14 = tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))),
% 0.61/0.70 inference(and_elim,[status(thm)],[43])).
% 0.61/0.70 tff(98,plain,
% 0.61/0.70 (t2tb(Q21!14) = t2tb(tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[97])).
% 0.61/0.70 tff(99,plain,
% 0.61/0.70 (t2tb(tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) = t2tb(Q21!14)),
% 0.61/0.70 inference(symmetry,[status(thm)],[98])).
% 0.61/0.70 tff(100,plain,
% 0.61/0.70 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(101,plain,
% 0.61/0.70 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(102,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bridgeR')).
% 0.61/0.70 tff(103,plain,
% 0.61/0.70 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.61/0.70 tff(104,plain,(
% 0.61/0.70 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.61/0.70 inference(skolemize,[status(sab)],[103])).
% 0.61/0.70 tff(105,plain,
% 0.61/0.70 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.61/0.70 tff(106,plain,
% 0.61/0.70 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) = cons(elt, t2tb1(X!21), t2tb(X3!20)))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(107,plain,
% 0.61/0.70 (t2tb(tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20)))) = cons(elt, t2tb1(X!21), t2tb(X3!20))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.61/0.70 tff(108,plain,
% 0.61/0.70 (cons(elt, t2tb1(X!21), t2tb(X3!20)) = t2tb(tb2t(cons(elt, t2tb1(X!21), t2tb(X3!20))))),
% 0.61/0.70 inference(symmetry,[status(thm)],[107])).
% 0.61/0.70 tff(109,plain,
% 0.61/0.70 (cons(elt, t2tb1(X!21), t2tb(X3!20)) = t2tb(Q21!14)),
% 0.61/0.70 inference(transitivity,[status(thm)],[108, 99])).
% 0.61/0.70 tff(110,plain,
% 0.61/0.70 (Q11!13 = tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.70 inference(and_elim,[status(thm)],[43])).
% 0.61/0.70 tff(111,plain,
% 0.61/0.70 (t2tb(Q11!13) = t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[110])).
% 0.61/0.70 tff(112,plain,
% 0.61/0.70 (t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) = t2tb(Q11!13)),
% 0.61/0.70 inference(symmetry,[status(thm)],[111])).
% 0.61/0.70 tff(113,plain,
% 0.61/0.70 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(114,plain,
% 0.61/0.70 (t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))) = cons(elt, t2tb1(X!26), t2tb(X2!25))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[113, 105])).
% 0.61/0.70 tff(115,plain,
% 0.61/0.70 (cons(elt, t2tb1(X!26), t2tb(X2!25)) = t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.70 inference(symmetry,[status(thm)],[114])).
% 0.61/0.70 tff(116,plain,
% 0.61/0.70 (cons(elt, t2tb1(X!26), t2tb(X2!25)) = t2tb(Q11!13)),
% 0.61/0.70 inference(transitivity,[status(thm)],[115, 112])).
% 0.61/0.70 tff(117,plain,
% 0.61/0.70 (infix_plpl(elt, cons(elt, t2tb1(X!26), t2tb(X2!25)), cons(elt, t2tb1(X!21), t2tb(X3!20))) = infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[116, 109])).
% 0.61/0.70 tff(118,plain,
% 0.61/0.70 (infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)) = infix_plpl(elt, cons(elt, t2tb1(X!26), t2tb(X2!25)), cons(elt, t2tb1(X!21), t2tb(X3!20)))),
% 0.61/0.70 inference(symmetry,[status(thm)],[117])).
% 0.61/0.70 tff(119,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))) <=> permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, cons(elt, t2tb1(X!26), t2tb(X2!25)), cons(elt, t2tb1(X!21), t2tb(X3!20))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[118])).
% 0.61/0.70 tff(120,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, cons(elt, t2tb1(X!26), t2tb(X2!25)), cons(elt, t2tb1(X!21), t2tb(X3!20)))) <=> permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))),
% 0.61/0.70 inference(symmetry,[status(thm)],[119])).
% 0.61/0.70 tff(121,plain,
% 0.61/0.70 (^[A: ty, X: uni, L1: uni, L2: uni] : refl(permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2))) <=> permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2))))),
% 0.61/0.70 inference(bind,[status(th)],[])).
% 0.61/0.70 tff(122,plain,
% 0.61/0.70 (![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))),
% 0.61/0.70 inference(quant_intro,[status(thm)],[121])).
% 0.61/0.70 tff(123,plain,
% 0.61/0.70 (![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(124,axiom,(![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_cons_append')).
% 0.61/0.70 tff(125,plain,
% 0.61/0.70 (![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.61/0.70 tff(126,plain,(
% 0.61/0.70 ![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))),
% 0.61/0.70 inference(skolemize,[status(sab)],[125])).
% 0.61/0.70 tff(127,plain,
% 0.61/0.70 (![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.61/0.70 tff(128,plain,
% 0.61/0.70 ((~![A: ty, X: uni, L1: uni, L2: uni] : permut(A, infix_plpl(A, cons(A, X, L1), L2), infix_plpl(A, L1, cons(A, X, L2)))) | permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, cons(elt, t2tb1(X!26), t2tb(X2!25)), cons(elt, t2tb1(X!21), t2tb(X3!20))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(129,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, cons(elt, t2tb1(X!26), t2tb(X2!25)), cons(elt, t2tb1(X!21), t2tb(X3!20))))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.61/0.70 tff(130,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[129, 120])).
% 0.61/0.70 tff(131,plain,
% 0.61/0.70 (^[A: ty, L1: uni, L2: uni] : refl(((~permut(A, L1, L2)) | permut(A, L2, L1)) <=> ((~permut(A, L1, L2)) | permut(A, L2, L1)))),
% 0.61/0.70 inference(bind,[status(th)],[])).
% 0.61/0.70 tff(132,plain,
% 0.61/0.70 (![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))),
% 0.61/0.70 inference(quant_intro,[status(thm)],[131])).
% 0.61/0.70 tff(133,plain,
% 0.61/0.70 (![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))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(134,plain,
% 0.61/0.70 (^[A: ty, L1: uni, L2: uni] : rewrite((permut(A, L1, L2) => permut(A, L2, L1)) <=> ((~permut(A, L1, L2)) | permut(A, L2, L1)))),
% 0.61/0.70 inference(bind,[status(th)],[])).
% 0.61/0.70 tff(135,plain,
% 0.61/0.70 (![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))),
% 0.61/0.70 inference(quant_intro,[status(thm)],[134])).
% 0.61/0.70 tff(136,axiom,(![A: ty, L1: uni, L2: uni] : (permut(A, L1, L2) => permut(A, L2, L1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_sym')).
% 0.61/0.70 tff(137,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.61/0.70 tff(138,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.61/0.70 tff(139,plain,(
% 0.61/0.70 ![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.61/0.70 inference(skolemize,[status(sab)],[138])).
% 0.61/0.70 tff(140,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.61/0.70 tff(141,plain,
% 0.61/0.70 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))) | permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))) | permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(142,plain,
% 0.61/0.70 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))) | permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(143,plain,
% 0.61/0.70 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))) | permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.61/0.70 tff(144,plain,
% 0.61/0.70 ((~permut(elt, infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)))) | permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.61/0.70 tff(145,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, cons(elt, t2tb1(X!21), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[144, 130])).
% 0.61/0.70 tff(146,plain,
% 0.61/0.70 (permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[145, 96])).
% 0.61/0.70 tff(147,plain,
% 0.61/0.70 (Q22!19 = X3!20),
% 0.61/0.70 inference(and_elim,[status(thm)],[43])).
% 0.61/0.70 tff(148,plain,
% 0.61/0.70 (t2tb(Q22!19) = t2tb(X3!20)),
% 0.61/0.70 inference(monotonicity,[status(thm)],[147])).
% 0.61/0.70 tff(149,plain,
% 0.61/0.70 (infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)) = infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[148])).
% 0.61/0.70 tff(150,plain,
% 0.61/0.70 (t2tb(X3!20) = t2tb(Q22!19)),
% 0.61/0.70 inference(symmetry,[status(thm)],[148])).
% 0.61/0.70 tff(151,plain,
% 0.61/0.70 (~((~(Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))))),
% 0.61/0.70 inference(and_elim,[status(thm)],[43])).
% 0.61/0.70 tff(152,plain,
% 0.61/0.70 (Q4!22 = tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))),
% 0.61/0.70 inference(or_elim,[status(thm)],[151])).
% 0.61/0.70 tff(153,plain,
% 0.61/0.70 (t2tb(Q4!22) = t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[152])).
% 0.61/0.70 tff(154,plain,
% 0.61/0.70 (infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)) = infix_plpl(elt, t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))), t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[153, 111])).
% 0.61/0.70 tff(155,plain,
% 0.61/0.70 (infix_plpl(elt, t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))), t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25))))) = infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13))),
% 0.61/0.70 inference(symmetry,[status(thm)],[154])).
% 0.61/0.70 tff(156,plain,
% 0.61/0.70 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))) = infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(157,plain,
% 0.61/0.70 (t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))) = infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[156, 105])).
% 0.61/0.70 tff(158,plain,
% 0.61/0.70 (infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))) = t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt)))))),
% 0.61/0.70 inference(symmetry,[status(thm)],[157])).
% 0.61/0.70 tff(159,plain,
% 0.61/0.70 (infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25))) = infix_plpl(elt, t2tb(tb2t(infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))))), t2tb(tb2t(cons(elt, t2tb1(X!26), t2tb(X2!25)))))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[158, 115])).
% 0.61/0.70 tff(160,plain,
% 0.61/0.70 (^[A: ty, L1: uni, L2: uni, L3: uni] : refl((infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3)) <=> (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3)))),
% 0.61/0.70 inference(bind,[status(th)],[])).
% 0.61/0.70 tff(161,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3)) <=> ![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))),
% 0.61/0.70 inference(quant_intro,[status(thm)],[160])).
% 0.61/0.70 tff(162,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3)) <=> ![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))),
% 0.61/0.70 inference(rewrite,[status(thm)],[])).
% 0.61/0.70 tff(163,axiom,(![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','append_assoc')).
% 0.61/0.70 tff(164,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.61/0.70 tff(165,plain,(
% 0.61/0.70 ![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))),
% 0.61/0.70 inference(skolemize,[status(sab)],[164])).
% 0.61/0.70 tff(166,plain,
% 0.61/0.70 (![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))),
% 0.61/0.70 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.61/0.70 tff(167,plain,
% 0.61/0.70 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))) | (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25))))),
% 0.61/0.70 inference(quant_inst,[status(thm)],[])).
% 0.61/0.70 tff(168,plain,
% 0.61/0.70 (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), cons(elt, t2tb1(O!18), nil(elt))), cons(elt, t2tb1(X!26), t2tb(X2!25)))),
% 0.61/0.70 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.61/0.70 tff(169,plain,
% 0.61/0.70 (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))) = infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13))),
% 0.61/0.70 inference(transitivity,[status(thm)],[168, 159, 155])).
% 0.61/0.70 tff(170,plain,
% 0.61/0.70 (infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))), t2tb(X3!20)) = infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19))),
% 0.61/0.70 inference(monotonicity,[status(thm)],[169, 150])).
% 0.61/0.70 tff(171,plain,
% 0.61/0.70 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))) | (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))), t2tb(X3!20)))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(172,plain,
% 0.61/0.71 (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25)))), t2tb(X3!20))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[171, 166])).
% 0.61/0.71 tff(173,plain,
% 0.61/0.71 (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20))),
% 0.61/0.71 inference(transitivity,[status(thm)],[172, 170, 149])).
% 0.61/0.71 tff(174,plain,
% 0.61/0.71 ((~![A: ty, L1: uni, L2: uni, L3: uni] : (infix_plpl(A, L1, infix_plpl(A, L2, L3)) = infix_plpl(A, infix_plpl(A, L1, L2), L3))) | (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(175,plain,
% 0.61/0.71 (infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))) = infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[174, 166])).
% 0.61/0.71 tff(176,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) <=> permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[175, 173])).
% 0.61/0.71 tff(177,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20))) <=> permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))),
% 0.61/0.71 inference(symmetry,[status(thm)],[176])).
% 0.61/0.71 tff(178,plain,
% 0.61/0.71 ((~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))) <=> (~permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[177])).
% 0.61/0.71 tff(179,plain,
% 0.61/0.71 (infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)) = infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19))),
% 0.61/0.71 inference(symmetry,[status(thm)],[149])).
% 0.61/0.71 tff(180,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))) <=> permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[179])).
% 0.61/0.71 tff(181,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))) <=> permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(symmetry,[status(thm)],[180])).
% 0.61/0.71 tff(182,plain,
% 0.61/0.71 ((~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))) <=> (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[181])).
% 0.61/0.71 tff(183,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))),
% 0.61/0.71 inference(and_elim,[status(thm)],[43])).
% 0.61/0.71 tff(184,plain,
% 0.61/0.71 (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))),
% 0.61/0.71 inference(or_elim,[status(thm)],[151])).
% 0.61/0.71 tff(185,plain,
% 0.61/0.71 (^[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))))),
% 0.61/0.71 inference(bind,[status(th)],[])).
% 0.61/0.71 tff(186,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(quant_intro,[status(thm)],[185])).
% 0.61/0.71 tff(187,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(188,plain,
% 0.61/0.71 (^[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)))))),
% 0.61/0.71 inference(bind,[status(th)],[])).
% 0.61/0.71 tff(189,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(quant_intro,[status(thm)],[188])).
% 0.61/0.71 tff(190,axiom,(![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L2) => (permut(A, L2, L3) => permut(A, L1, L3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_trans')).
% 0.61/0.71 tff(191,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.61/0.71 tff(192,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.61/0.71 tff(193,plain,(
% 0.61/0.71 ![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.61/0.71 inference(skolemize,[status(sab)],[192])).
% 0.61/0.71 tff(194,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni, L3: uni] : (permut(A, L1, L3) | (~permut(A, L2, L3)) | (~permut(A, L1, L2)))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.61/0.71 tff(195,plain,
% 0.61/0.71 (((~![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, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))))) <=> ((~![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, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(196,plain,
% 0.61/0.71 ((~![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, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(197,plain,
% 0.61/0.71 ((~![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, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, t2tb(Q1!12), t2tb(Q2!11)))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.61/0.71 tff(198,plain,
% 0.61/0.71 (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(Q22!19)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[197, 194, 184, 183])).
% 0.61/0.71 tff(199,plain,
% 0.61/0.71 (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[198, 182])).
% 0.61/0.71 tff(200,plain,
% 0.61/0.71 (((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))))) <=> ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(201,plain,
% 0.61/0.71 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | ((~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(202,plain,
% 0.61/0.71 ((~![A: ty, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, L2, L1))) | (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.61/0.71 tff(203,plain,
% 0.61/0.71 ((~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))) | permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)), infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[202, 140])).
% 0.61/0.71 tff(204,plain,
% 0.61/0.71 (~permut(elt, infix_plpl(elt, infix_plpl(elt, t2tb(Q3!15), t2tb(Q11!13)), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, t2tb(Q4!22), t2tb(Q11!13)), t2tb(X3!20)))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[203, 199])).
% 0.61/0.71 tff(205,plain,
% 0.61/0.71 (~permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[204, 178])).
% 0.61/0.71 tff(206,plain,
% 0.61/0.71 ((~![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(elt, nil(elt), t2tb(Q3!15)) = t2tb(Q3!15))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), t2tb(Q3!15)) = cons(elt, X, infix_plpl(elt, X1, t2tb(Q3!15)))))))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(207,plain,
% 0.61/0.71 (~((~(infix_plpl(elt, nil(elt), t2tb(Q3!15)) = t2tb(Q3!15))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), t2tb(Q3!15)) = cons(elt, X, infix_plpl(elt, X1, t2tb(Q3!15))))))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[206, 13])).
% 0.61/0.71 tff(208,plain,
% 0.61/0.71 (((~(infix_plpl(elt, nil(elt), t2tb(Q3!15)) = t2tb(Q3!15))) | (~![X: uni, X1: uni] : (infix_plpl(elt, cons(elt, X, X1), t2tb(Q3!15)) = cons(elt, X, infix_plpl(elt, X1, t2tb(Q3!15)))))) | (infix_plpl(elt, nil(elt), t2tb(Q3!15)) = t2tb(Q3!15))),
% 0.61/0.71 inference(tautology,[status(thm)],[])).
% 0.61/0.71 tff(209,plain,
% 0.61/0.71 (infix_plpl(elt, nil(elt), t2tb(Q3!15)) = t2tb(Q3!15)),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.61/0.71 tff(210,plain,
% 0.61/0.71 (^[A: ty, L: uni] : refl((infix_plpl(A, L, nil(A)) = L) <=> (infix_plpl(A, L, nil(A)) = L))),
% 0.61/0.71 inference(bind,[status(th)],[])).
% 0.61/0.71 tff(211,plain,
% 0.61/0.71 (![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L) <=> ![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)),
% 0.61/0.71 inference(quant_intro,[status(thm)],[210])).
% 0.61/0.71 tff(212,plain,
% 0.61/0.71 (![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L) <=> ![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(213,axiom,(![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','append_l_nil')).
% 0.61/0.71 tff(214,plain,
% 0.61/0.71 (![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.61/0.71 tff(215,plain,(
% 0.61/0.71 ![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)),
% 0.61/0.71 inference(skolemize,[status(sab)],[214])).
% 0.61/0.71 tff(216,plain,
% 0.61/0.71 (![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.61/0.71 tff(217,plain,
% 0.61/0.71 ((~![A: ty, L: uni] : (infix_plpl(A, L, nil(A)) = L)) | (infix_plpl(elt, t2tb(Q3!15), nil(elt)) = t2tb(Q3!15))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(218,plain,
% 0.61/0.71 (infix_plpl(elt, t2tb(Q3!15), nil(elt)) = t2tb(Q3!15)),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.61/0.71 tff(219,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, t2tb(Q3!15), nil(elt)), infix_plpl(elt, nil(elt), t2tb(Q3!15))) <=> permut(elt, t2tb(Q3!15), t2tb(Q3!15))),
% 0.61/0.71 inference(monotonicity,[status(thm)],[218, 209])).
% 0.61/0.71 tff(220,plain,
% 0.61/0.71 (^[A: ty, L1: uni, L2: uni] : refl(permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1)) <=> permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1)))),
% 0.61/0.71 inference(bind,[status(th)],[])).
% 0.61/0.71 tff(221,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1)) <=> ![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))),
% 0.61/0.71 inference(quant_intro,[status(thm)],[220])).
% 0.61/0.71 tff(222,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1)) <=> ![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(223,axiom,(![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permut_append_swap')).
% 0.61/0.71 tff(224,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.61/0.71 tff(225,plain,(
% 0.61/0.71 ![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))),
% 0.61/0.71 inference(skolemize,[status(sab)],[224])).
% 0.61/0.71 tff(226,plain,
% 0.61/0.71 (![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.61/0.71 tff(227,plain,
% 0.61/0.71 ((~![A: ty, L1: uni, L2: uni] : permut(A, infix_plpl(A, L1, L2), infix_plpl(A, L2, L1))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), nil(elt)), infix_plpl(elt, nil(elt), t2tb(Q3!15)))),
% 0.61/0.71 inference(quant_inst,[status(thm)],[])).
% 0.61/0.71 tff(228,plain,
% 0.61/0.71 (permut(elt, infix_plpl(elt, t2tb(Q3!15), nil(elt)), infix_plpl(elt, nil(elt), t2tb(Q3!15)))),
% 0.61/0.71 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.61/0.71 tff(229,plain,
% 0.61/0.71 (permut(elt, t2tb(Q3!15), t2tb(Q3!15))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[228, 219])).
% 0.61/0.71 tff(230,plain,
% 0.61/0.71 (^[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))))),
% 0.61/0.71 inference(bind,[status(th)],[])).
% 0.61/0.71 tff(231,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(quant_intro,[status(thm)],[230])).
% 0.61/0.71 tff(232,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(rewrite,[status(thm)],[])).
% 0.61/0.71 tff(233,plain,
% 0.61/0.71 (^[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)))))),
% 0.61/0.71 inference(bind,[status(th)],[])).
% 0.61/0.71 tff(234,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(quant_intro,[status(thm)],[233])).
% 0.61/0.71 tff(235,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/sandbox2/benchmark/theBenchmark.p','permut_append')).
% 0.61/0.71 tff(236,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.71 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.61/0.71 tff(237,plain,
% 0.61/0.71 (![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)))),
% 0.61/0.72 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.61/0.72 tff(238,plain,(
% 0.61/0.72 ![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)))),
% 0.61/0.72 inference(skolemize,[status(sab)],[237])).
% 0.61/0.72 tff(239,plain,
% 0.61/0.72 (![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)))),
% 0.61/0.72 inference(modus_ponens,[status(thm)],[238, 231])).
% 0.61/0.72 tff(240,plain,
% 0.61/0.72 (((~![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(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))))) <=> ((~![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(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))))),
% 0.61/0.72 inference(rewrite,[status(thm)],[])).
% 0.61/0.72 tff(241,plain,
% 0.61/0.72 ((permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, t2tb(Q3!15), t2tb(Q3!15)))) <=> ((~permut(elt, t2tb(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))))),
% 0.61/0.72 inference(rewrite,[status(thm)],[])).
% 0.61/0.72 tff(242,plain,
% 0.61/0.72 (((~![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(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, t2tb(Q3!15), t2tb(Q3!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(elt, t2tb(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[241])).
% 0.73/0.72 tff(243,plain,
% 0.73/0.72 (((~![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(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, t2tb(Q3!15), t2tb(Q3!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(elt, t2tb(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))))),
% 0.73/0.72 inference(transitivity,[status(thm)],[242, 240])).
% 0.73/0.72 tff(244,plain,
% 0.73/0.72 ((~![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(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, t2tb(Q3!15), t2tb(Q3!15))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(245,plain,
% 0.73/0.72 ((~![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(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.73/0.72 tff(246,plain,
% 0.73/0.72 ((~permut(elt, t2tb(Q3!15), t2tb(Q3!15))) | permut(elt, infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14))), infix_plpl(elt, t2tb(Q3!15), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20)))) | (~permut(elt, infix_plpl(elt, t2tb(Q11!13), t2tb(Q21!14)), infix_plpl(elt, infix_plpl(elt, cons(elt, t2tb1(O!18), nil(elt)), cons(elt, t2tb1(X!26), t2tb(X2!25))), t2tb(X3!20))))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[245, 239])).
% 0.73/0.72 tff(247,plain,
% 0.73/0.72 ($false),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[246, 229, 205, 146])).
% 0.73/0.72 % SZS output end Proof
%------------------------------------------------------------------------------