TSTP Solution File: SWW625_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW625_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW625_2 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 20:46:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(mem_type, type, (
% 0.21/0.49 mem: ( ty * uni * uni ) > $o)).
% 0.21/0.49 tff(reverse_type, type, (
% 0.21/0.49 reverse: ( ty * uni ) > uni)).
% 0.21/0.49 tff(cons_type, type, (
% 0.21/0.49 cons: ( ty * uni * uni ) > uni)).
% 0.21/0.49 tff(t2tb_type, type, (
% 0.21/0.49 t2tb: list_elt > uni)).
% 0.21/0.49 tff(tptp_fun_X1_14_type, type, (
% 0.21/0.49 tptp_fun_X1_14: list_elt)).
% 0.21/0.49 tff(t2tb1_type, type, (
% 0.21/0.49 t2tb1: elt > uni)).
% 0.21/0.49 tff(tptp_fun_X_15_type, type, (
% 0.21/0.49 tptp_fun_X_15: elt)).
% 0.21/0.49 tff(elt1_type, type, (
% 0.21/0.49 elt1: ty)).
% 0.21/0.49 tff(tptp_fun_X_9_type, type, (
% 0.21/0.49 tptp_fun_X_9: ( list_elt * list_elt ) > elt)).
% 0.21/0.49 tff(tb2t_type, type, (
% 0.21/0.49 tb2t: uni > list_elt)).
% 0.21/0.49 tff(tptp_fun_Accu_11_type, type, (
% 0.21/0.49 tptp_fun_Accu_11: list_elt)).
% 0.21/0.49 tff(tptp_fun_L2_12_type, type, (
% 0.21/0.49 tptp_fun_L2_12: list_elt)).
% 0.21/0.49 tff(nil_type, type, (
% 0.21/0.49 nil: ty > uni)).
% 0.21/0.49 tff(tptp_fun_L1_13_type, type, (
% 0.21/0.49 tptp_fun_L1_13: list_elt)).
% 0.21/0.49 tff(sorted_type, type, (
% 0.21/0.49 sorted: list_elt > $o)).
% 0.21/0.49 tff(rev_append_type, type, (
% 0.21/0.49 rev_append: ( ty * uni * uni ) > uni)).
% 0.21/0.49 tff(le_type, type, (
% 0.21/0.49 le: ( elt * elt ) > $o)).
% 0.21/0.49 tff(tptp_fun_Y_8_type, type, (
% 0.21/0.49 tptp_fun_Y_8: ( list_elt * list_elt ) > elt)).
% 0.21/0.49 tff(infix_plpl_type, type, (
% 0.21/0.49 infix_plpl: ( ty * uni * uni ) > uni)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 (^[A: ty, L: uni, X: uni] : refl((mem(A, X, L) <=> mem(A, X, reverse(A, L))) <=> (mem(A, X, L) <=> mem(A, X, reverse(A, L))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L))) <=> ![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L))) <=> ![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reverse_mem')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,(
% 0.21/0.49 ![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 ((~![A: ty, L: uni, X: uni] : (mem(A, X, L) <=> mem(A, X, reverse(A, L)))) | (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14))) <=> mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14))) <=> mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(12,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.49 tff(14,plain,(
% 0.21/0.49 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.49 inference(skolemize,[status(sab)],[13])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))) = cons(elt1, t2tb1(X!15), t2tb(X1!14)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (t2tb(tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))) = cons(elt1, t2tb1(X!15), t2tb(X1!14))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (((sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))) <=> (sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 ((~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14))))))) <=> (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 ((sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) <=> (sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (((sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))) <=> ((sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[20, 19])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (((sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))) <=> (sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[21, 18])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 ((~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))) <=> (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 ((~![L1: list_elt, L2: list_elt, Accu: list_elt] : (((((sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1))))) & sorted(tb2t(reverse(elt1, t2tb(L2))))) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(Accu)) => (mem(elt1, t2tb1(Y), t2tb(L1)) => le(Y, X)))) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(Accu)) => (mem(elt1, t2tb1(Y), t2tb(L2)) => le(Y, X)))) => ![X: elt, X1: list_elt] : ((L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))) => ((L1 = tb2t(nil(elt1))) => sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))))))) <=> (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(25,axiom,(~![L1: list_elt, L2: list_elt, Accu: list_elt] : (((((sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1))))) & sorted(tb2t(reverse(elt1, t2tb(L2))))) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(Accu)) => (mem(elt1, t2tb1(Y), t2tb(L1)) => le(Y, X)))) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(Accu)) => (mem(elt1, t2tb1(Y), t2tb(L2)) => le(Y, X)))) => ![X: elt, X1: list_elt] : ((L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))) => ((L1 = tb2t(nil(elt1))) => sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_rev_merge_rev')).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.21/0.50 tff(28,plain,
% 0.21/0.50 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.50 tff(29,plain,
% 0.21/0.50 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.21/0.50 tff(30,plain,
% 0.21/0.50 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.21/0.50 tff(31,plain,
% 0.21/0.50 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.21/0.50 tff(32,plain,
% 0.21/0.50 (~![L1: list_elt, L2: list_elt, Accu: list_elt] : ((~(sorted(Accu) & sorted(tb2t(reverse(elt1, t2tb(L1)))) & sorted(tb2t(reverse(elt1, t2tb(L2)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1))) | (~mem(elt1, t2tb1(X), t2tb(Accu)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu))) | (~mem(elt1, t2tb1(Y), t2tb(L2)))))) | ![X: elt, X1: list_elt] : (sorted(tb2t(rev_append(elt1, t2tb(L2), t2tb(Accu)))) | (~(L1 = tb2t(nil(elt1)))) | (~(L2 = tb2t(cons(elt1, t2tb1(X), t2tb(X1)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.21/0.50 tff(33,plain,
% 0.21/0.50 (sorted(Accu!11) & sorted(tb2t(reverse(elt1, t2tb(L1!13)))) & sorted(tb2t(reverse(elt1, t2tb(L2!12)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(Y), t2tb(L1!13))) | (~mem(elt1, t2tb1(X), t2tb(Accu!11)))) & ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))) & (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.21/0.50 tff(34,plain,
% 0.21/0.50 (~(sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) | (~(L1!13 = tb2t(nil(elt1)))) | (~(L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14))))))),
% 0.21/0.50 inference(and_elim,[status(thm)],[33])).
% 0.21/0.50 tff(35,plain,
% 0.21/0.50 (L2!12 = tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14)))),
% 0.21/0.50 inference(or_elim,[status(thm)],[34])).
% 0.21/0.50 tff(36,plain,
% 0.21/0.50 (t2tb(L2!12) = t2tb(tb2t(cons(elt1, t2tb1(X!15), t2tb(X1!14))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.50 tff(37,plain,
% 0.21/0.50 (t2tb(L2!12) = cons(elt1, t2tb1(X!15), t2tb(X1!14))),
% 0.21/0.50 inference(transitivity,[status(thm)],[36, 17])).
% 0.21/0.50 tff(38,plain,
% 0.21/0.50 (reverse(elt1, t2tb(L2!12)) = reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.50 tff(39,plain,
% 0.21/0.50 (tb2t(reverse(elt1, t2tb(L2!12))) = tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.50 tff(40,plain,
% 0.21/0.50 (tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))) = tb2t(reverse(elt1, t2tb(L2!12)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[39])).
% 0.21/0.50 tff(41,plain,
% 0.21/0.50 (t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))) = t2tb(tb2t(reverse(elt1, t2tb(L2!12))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (t2tb(tb2t(reverse(elt1, t2tb(L2!12)))) = t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[41])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(reverse(elt1, t2tb(L2!12)))) = reverse(elt1, t2tb(L2!12)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 (t2tb(tb2t(reverse(elt1, t2tb(L2!12)))) = reverse(elt1, t2tb(L2!12))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[43, 15])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 (reverse(elt1, t2tb(L2!12)) = t2tb(tb2t(reverse(elt1, t2tb(L2!12))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[44])).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))) = reverse(elt1, t2tb(L2!12))),
% 0.21/0.50 inference(symmetry,[status(thm)],[38])).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 (reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))) = t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[46, 45, 42])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))) <=> mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) <=> mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))),
% 0.21/0.50 inference(symmetry,[status(thm)],[48])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 (^[L1: list_elt, L2: list_elt] : rewrite((~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> ![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 (^[L1: list_elt, L2: list_elt] : refl((~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> ![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 (^[L1: list_elt, L2: list_elt] : rewrite((~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> ![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))) <=> ![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[55, 53])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 (^[L1: list_elt, L2: list_elt] : trans(monotonicity(trans(monotonicity(rewrite((~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))) <=> (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))), ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) <=> (sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))))), rewrite((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) <=> (sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))), ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) <=> (sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))))), trans(monotonicity(rewrite((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))), (((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))) <=> ((~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))))), rewrite(((~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))) <=> ((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))), (((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))) <=> ((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))), (((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))) <=> ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))))), rewrite(((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1)))))) <=> (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))), (((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))) <=> (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))) <=> ![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (^[L1: list_elt, L2: list_elt] : rewrite(((((~sorted(L1)) | (~sorted(L2)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) | sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))) <=> ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : ((((~sorted(L1)) | (~sorted(L2)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) | sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))) <=> ![L1: list_elt, L2: list_elt] : ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) <=> ![L1: list_elt, L2: list_elt] : ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (^[L1: list_elt, L2: list_elt] : rewrite((((sorted(L1) & sorted(L2)) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(L1)) => (mem(elt1, t2tb1(Y), t2tb(L2)) => le(X, Y)))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) <=> ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (![L1: list_elt, L2: list_elt] : (((sorted(L1) & sorted(L2)) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(L1)) => (mem(elt1, t2tb1(Y), t2tb(L2)) => le(X, Y)))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) <=> ![L1: list_elt, L2: list_elt] : ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.51 tff(64,axiom,(![L1: list_elt, L2: list_elt] : (((sorted(L1) & sorted(L2)) & ![X: elt, Y: elt] : (mem(elt1, t2tb1(X), t2tb(L1)) => (mem(elt1, t2tb1(Y), t2tb(L2)) => le(X, Y)))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sorted_append')).
% 0.21/0.51 tff(65,plain,
% 0.21/0.51 (![L1: list_elt, L2: list_elt] : ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.51 tff(66,plain,
% 0.21/0.51 (![L1: list_elt, L2: list_elt] : ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.51 tff(67,plain,(
% 0.21/0.51 ![L1: list_elt, L2: list_elt] : ((((~sorted(L1)) | (~sorted(L2)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) | sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[66])).
% 0.21/0.51 tff(68,plain,
% 0.21/0.51 (![L1: list_elt, L2: list_elt] : ((sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1)))))) & ((sorted(L1) & sorted(L2) & ![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.51 tff(69,plain,
% 0.21/0.51 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.21/0.51 tff(70,plain,
% 0.21/0.51 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1))))) | (~sorted(L1))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[69, 56])).
% 0.21/0.51 tff(71,plain,
% 0.21/0.51 (![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[70, 51])).
% 0.21/0.51 tff(72,plain,
% 0.21/0.51 (((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))))) <=> ((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(73,plain,
% 0.21/0.51 ((~((~(sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))))))) <=> (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(74,plain,
% 0.21/0.51 (((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))))) <=> ((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.51 tff(75,plain,
% 0.21/0.51 (((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))))) <=> ((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[74, 72])).
% 0.21/0.51 tff(76,plain,
% 0.21/0.51 ((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(77,plain,
% 0.21/0.52 ((~![L1: list_elt, L2: list_elt] : (~((~(sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2)))) | (~sorted(L2)) | (~sorted(L1)) | (~(le(tptp_fun_X_9(L2, L1), tptp_fun_Y_8(L2, L1)) | (~mem(elt1, t2tb1(tptp_fun_Y_8(L2, L1)), t2tb(L2))) | (~mem(elt1, t2tb1(tptp_fun_X_9(L2, L1)), t2tb(L1))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(L1), t2tb(L2))))) | (~((~sorted(L2)) | (~sorted(L1)) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(L2))) | (~mem(elt1, t2tb1(X), t2tb(L1)))))))))))) | (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.52 tff(78,plain,
% 0.21/0.52 (~((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[77, 71])).
% 0.21/0.52 tff(79,plain,
% 0.21/0.52 (((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~((~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))) | (~((~sorted(Accu!11)) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~![X: elt, Y: elt] : (le(X, Y) | (~mem(elt1, t2tb1(Y), t2tb(Accu!11))) | (~mem(elt1, t2tb1(X), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))))))) | ((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(80,plain,
% 0.21/0.52 ((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.52 tff(81,plain,
% 0.21/0.52 (^[A: ty, R: uni, S: uni] : refl((rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S)) <=> (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(82,plain,
% 0.21/0.52 (![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S)) <=> ![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.52 tff(83,plain,
% 0.21/0.52 (![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S)) <=> ![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(84,axiom,(![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rev_append_def1')).
% 0.21/0.52 tff(85,plain,
% 0.21/0.52 (![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.52 tff(86,plain,(
% 0.21/0.52 ![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))),
% 0.21/0.52 inference(skolemize,[status(sab)],[85])).
% 0.21/0.52 tff(87,plain,
% 0.21/0.52 (![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.52 tff(88,plain,
% 0.21/0.52 ((~![A: ty, R: uni, S: uni] : (rev_append(A, R, S) = infix_plpl(A, reverse(A, R), S))) | (rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)) = infix_plpl(elt1, reverse(elt1, t2tb(L2!12)), t2tb(Accu!11)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(89,plain,
% 0.21/0.52 (rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)) = infix_plpl(elt1, reverse(elt1, t2tb(L2!12)), t2tb(Accu!11))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.52 tff(90,plain,
% 0.21/0.52 (infix_plpl(elt1, reverse(elt1, t2tb(L2!12)), t2tb(Accu!11)) = rev_append(elt1, t2tb(L2!12), t2tb(Accu!11))),
% 0.21/0.52 inference(symmetry,[status(thm)],[89])).
% 0.21/0.52 tff(91,plain,
% 0.21/0.52 (t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))) = reverse(elt1, t2tb(L2!12))),
% 0.21/0.52 inference(transitivity,[status(thm)],[41, 44])).
% 0.21/0.52 tff(92,plain,
% 0.21/0.52 (infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)) = infix_plpl(elt1, reverse(elt1, t2tb(L2!12)), t2tb(Accu!11))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.52 tff(93,plain,
% 0.21/0.52 (infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)) = rev_append(elt1, t2tb(L2!12), t2tb(Accu!11))),
% 0.21/0.52 inference(transitivity,[status(thm)],[92, 90])).
% 0.21/0.52 tff(94,plain,
% 0.21/0.52 (tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))) = tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.52 tff(95,plain,
% 0.21/0.52 (sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) <=> sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[94])).
% 0.21/0.52 tff(96,plain,
% 0.21/0.52 (sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11)))) <=> sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))),
% 0.21/0.52 inference(symmetry,[status(thm)],[95])).
% 0.21/0.52 tff(97,plain,
% 0.21/0.52 ((~sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11))))) <=> (~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.52 tff(98,plain,
% 0.21/0.52 (~sorted(tb2t(rev_append(elt1, t2tb(L2!12), t2tb(Accu!11))))),
% 0.21/0.52 inference(or_elim,[status(thm)],[34])).
% 0.21/0.52 tff(99,plain,
% 0.21/0.52 (~sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.52 tff(100,plain,
% 0.21/0.52 (sorted(tb2t(reverse(elt1, t2tb(L2!12)))) <=> sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.52 tff(101,plain,
% 0.21/0.52 (sorted(tb2t(reverse(elt1, t2tb(L2!12))))),
% 0.21/0.52 inference(and_elim,[status(thm)],[33])).
% 0.21/0.52 tff(102,plain,
% 0.21/0.52 (sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.52 tff(103,plain,
% 0.21/0.52 (sorted(Accu!11)),
% 0.21/0.52 inference(and_elim,[status(thm)],[33])).
% 0.21/0.52 tff(104,plain,
% 0.21/0.52 ((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | (~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(105,plain,
% 0.21/0.52 ((~((~sorted(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~sorted(Accu!11)) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))))) | sorted(tb2t(infix_plpl(elt1, t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), t2tb(Accu!11)))) | (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[104, 103, 102])).
% 0.21/0.52 tff(106,plain,
% 0.21/0.52 (~(le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[105, 99, 80])).
% 0.21/0.52 tff(107,plain,
% 0.21/0.52 ((le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))) | mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(108,plain,
% 0.21/0.52 (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.52 tff(109,plain,
% 0.21/0.52 (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[108, 49])).
% 0.21/0.52 tff(110,plain,
% 0.21/0.52 (mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12)) <=> mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.52 tff(111,plain,
% 0.21/0.52 ((~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12))) <=> (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[110])).
% 0.21/0.52 tff(112,plain,
% 0.21/0.52 ((le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))) | mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(113,plain,
% 0.21/0.52 (mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[112, 106])).
% 0.21/0.52 tff(114,plain,
% 0.21/0.52 ((le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))) | (~le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(115,plain,
% 0.21/0.52 (~le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[114, 106])).
% 0.21/0.52 tff(116,plain,
% 0.21/0.52 (^[X: elt, Y: elt] : refl((le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))) <=> (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(117,plain,
% 0.21/0.52 (![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12)))) <=> ![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.52 tff(118,plain,
% 0.21/0.52 (![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))),
% 0.21/0.52 inference(and_elim,[status(thm)],[33])).
% 0.21/0.52 tff(119,plain,
% 0.21/0.52 (![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.52 tff(120,plain,
% 0.21/0.52 (((~![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) | (le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12))))) <=> ((~![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) | le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(121,plain,
% 0.21/0.52 ((~![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) | (le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(122,plain,
% 0.21/0.52 ((~![X: elt, Y: elt] : (le(Y, X) | (~mem(elt1, t2tb1(X), t2tb(Accu!11))) | (~mem(elt1, t2tb1(Y), t2tb(L2!12))))) | le(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14))))), tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | (~mem(elt1, t2tb1(tptp_fun_Y_8(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(Accu!11))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.52 tff(123,plain,
% 0.21/0.52 (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), t2tb(L2!12))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[122, 119, 115, 113])).
% 0.21/0.53 tff(124,plain,
% 0.21/0.53 (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[123, 111])).
% 0.21/0.53 tff(125,plain,
% 0.21/0.53 ((~(mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14))) <=> mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))) | mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), cons(elt1, t2tb1(X!15), t2tb(X1!14))) | (~mem(elt1, t2tb1(tptp_fun_X_9(Accu!11, tb2t(reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))), reverse(elt1, cons(elt1, t2tb1(X!15), t2tb(X1!14)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(126,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[125, 124, 109, 9])).
% 0.21/0.53 % SZS output end Proof
%------------------------------------------------------------------------------