TSTP Solution File: SWW638_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW638_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:59:31 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW638_2 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:39:25 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(concat1_type, type, (
% 0.19/0.43 concat1: ( regexp1 * regexp1 ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_X1_18_type, type, (
% 0.19/0.43 tptp_fun_X1_18: regexp1)).
% 0.19/0.43 tff(tptp_fun_X_19_type, type, (
% 0.19/0.43 tptp_fun_X_19: regexp1)).
% 0.19/0.43 tff(alt1_type, type, (
% 0.19/0.43 alt1: ( regexp1 * regexp1 ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_R2_7_type, type, (
% 0.19/0.43 tptp_fun_R2_7: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tb2t_type, type, (
% 0.19/0.43 tb2t: uni > list_char)).
% 0.19/0.43 tff(nil_type, type, (
% 0.19/0.43 nil: ty > uni)).
% 0.19/0.43 tff(char1_type, type, (
% 0.19/0.43 char1: ty)).
% 0.19/0.43 tff(tptp_fun_R1_8_type, type, (
% 0.19/0.43 tptp_fun_R1_8: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_W_9_type, type, (
% 0.19/0.43 tptp_fun_W_9: ( regexp1 * list_char ) > list_char)).
% 0.19/0.43 tff(mem2_type, type, (
% 0.19/0.43 mem2: ( list_char * regexp1 ) > $o)).
% 0.19/0.43 tff(star1_type, type, (
% 0.19/0.43 star1: regexp1 > regexp1)).
% 0.19/0.43 tff(tptp_fun_R_14_type, type, (
% 0.19/0.43 tptp_fun_R_14: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(infix_plpl_type, type, (
% 0.19/0.43 infix_plpl: ( ty * uni * uni ) > uni)).
% 0.19/0.43 tff(t2tb_type, type, (
% 0.19/0.43 t2tb: list_char > uni)).
% 0.19/0.43 tff(tptp_fun_W2_15_type, type, (
% 0.19/0.43 tptp_fun_W2_15: ( regexp1 * list_char ) > list_char)).
% 0.19/0.43 tff(tptp_fun_W1_16_type, type, (
% 0.19/0.43 tptp_fun_W1_16: ( regexp1 * list_char ) > list_char)).
% 0.19/0.43 tff(tptp_fun_R2_4_type, type, (
% 0.19/0.43 tptp_fun_R2_4: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_R1_5_type, type, (
% 0.19/0.43 tptp_fun_R1_5: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_W_6_type, type, (
% 0.19/0.43 tptp_fun_W_6: ( regexp1 * list_char ) > list_char)).
% 0.19/0.43 tff(char3_type, type, (
% 0.19/0.43 char3: char2 > regexp1)).
% 0.19/0.43 tff(tptp_fun_C_3_type, type, (
% 0.19/0.43 tptp_fun_C_3: ( regexp1 * list_char ) > char2)).
% 0.19/0.43 tff(cons_type, type, (
% 0.19/0.43 cons: ( ty * uni * uni ) > uni)).
% 0.19/0.43 tff(t2tb1_type, type, (
% 0.19/0.43 t2tb1: char2 > uni)).
% 0.19/0.43 tff(tptp_fun_R_2_type, type, (
% 0.19/0.43 tptp_fun_R_2: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_R2_10_type, type, (
% 0.19/0.43 tptp_fun_R2_10: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_R1_11_type, type, (
% 0.19/0.43 tptp_fun_R1_11: ( regexp1 * list_char ) > regexp1)).
% 0.19/0.43 tff(tptp_fun_W2_12_type, type, (
% 0.19/0.43 tptp_fun_W2_12: ( regexp1 * list_char ) > list_char)).
% 0.19/0.43 tff(tptp_fun_W1_13_type, type, (
% 0.19/0.43 tptp_fun_W1_13: ( regexp1 * list_char ) > list_char)).
% 0.19/0.43 tff(concat_proj_21_type, type, (
% 0.19/0.43 concat_proj_21: regexp1 > regexp1)).
% 0.19/0.43 tff(length1_type, type, (
% 0.19/0.43 length1: ( ty * uni ) > $int)).
% 0.19/0.43 tff(true1_type, type, (
% 0.19/0.43 true1: bool1)).
% 0.19/0.43 tff(tptp_fun_Result1_20_type, type, (
% 0.19/0.43 tptp_fun_Result1_20: bool1)).
% 0.19/0.43 tff(tptp_fun_Result_17_type, type, (
% 0.19/0.43 tptp_fun_Result_17: bool1)).
% 0.19/0.43 tff(epsilon1_type, type, (
% 0.19/0.43 epsilon1: regexp1)).
% 0.19/0.43 tff(1,assumption,(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))), introduced(assumption)).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (^[U: regexp1, U1: regexp1, V: regexp1] : refl((~(concat1(U, U1) = star1(V))) <=> (~(concat1(U, U1) = star1(V))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V))) <=> ![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V))) <=> ![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(5,axiom,(![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','concat_Star')).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.43 tff(7,plain,(
% 0.19/0.43 ![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[6])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 ((~![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.43 tff(11,plain,(~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))) | (concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 ((alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)) <=> (concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(commutativity,[status(thm)],[])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 ((~(alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18))) <=> (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.43 tff(16,assumption,(alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)), introduced(assumption)).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (^[U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : refl((~(alt1(U, U1) = concat1(V, V1))) <=> (~(alt1(U, U1) = concat1(V, V1))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1))) <=> ![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1))) <=> ![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(20,axiom,(![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','alt_Concat')).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.43 tff(22,plain,(
% 0.19/0.43 ![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 ((~![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))) | (~(alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[24, 23, 16])).
% 0.19/0.43 tff(26,plain,(~(alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 15])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1))))))) | (concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 ((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 ((char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)) <=> (concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(commutativity,[status(thm)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~(char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18))) <=> (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.43 tff(32,assumption,(char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)), introduced(assumption)).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (^[U: char2, V: regexp1, V1: regexp1] : refl((~(char3(U) = concat1(V, V1))) <=> (~(char3(U) = concat1(V, V1))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1))) <=> ![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1))) <=> ![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(36,axiom,(![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','char_Concat')).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.43 tff(38,plain,(
% 0.19/0.43 ![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[37])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 ((~![U: char2, V: regexp1, V1: regexp1] : (~(char3(U) = concat1(V, V1)))) | (~(char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[40, 39, 32])).
% 0.19/0.43 tff(42,plain,(~(char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[42, 31])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1))))))) | (concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 ((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.43 tff(46,assumption,(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))), introduced(assumption)).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 ((~![U: regexp1, U1: regexp1, V: regexp1] : (~(concat1(U, U1) = star1(V)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[47, 8, 46])).
% 0.19/0.43 tff(49,plain,(~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (^[U: regexp1, U1: regexp1] : refl((concat_proj_21(concat1(U, U1)) = U1) <=> (concat_proj_21(concat1(U, U1)) = U1))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1) <=> ![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1) <=> ![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,axiom,(![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','concat_proj_2_def')).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.43 tff(55,plain,(
% 0.19/0.43 ![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)),
% 0.19/0.43 inference(skolemize,[status(sab)],[54])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 ((~![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)) | (concat_proj_21(concat1(X!19, X1!18)) = X1!18)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (concat_proj_21(concat1(X!19, X1!18)) = X1!18),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.43 tff(59,assumption,(~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))), introduced(assumption)).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))))) | (concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)),
% 0.19/0.44 inference(symmetry,[status(thm)],[61])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (concat_proj_21(concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) = concat_proj_21(concat1(X!19, X1!18))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~![U: regexp1, U1: regexp1] : (concat_proj_21(concat1(U, U1)) = U1)) | (concat_proj_21(concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) = tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (concat_proj_21(concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) = tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[64, 56])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 (tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))) = concat_proj_21(concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.44 inference(symmetry,[status(thm)],[65])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))) = X1!18),
% 0.19/0.44 inference(transitivity,[status(thm)],[66, 63, 58])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (^[A: ty, L: uni] : refl(((length1(A, L) = 0) <=> (L = nil(A))) <=> ((length1(A, L) = 0) <=> (L = nil(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A))) <=> ![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A))) <=> ![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(71,axiom,(![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_nil')).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.44 tff(73,plain,(
% 0.19/0.44 ![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 ((~![A: ty, L: uni] : ((length1(A, L) = 0) <=> (L = nil(A)))) | ((length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0) <=> (t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))) = nil(char1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 ((length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0) <=> (t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))) = nil(char1))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (^[A: ty] : refl((~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))) <=> (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))) <=> ![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (^[A: ty] : rewrite((~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))) <=> (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))) <=> ![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))) <=> ![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (^[A: ty] : rewrite(((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)) <=> (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)) <=> ![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (^[A: ty] : rewrite(((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, cons(A, X, X1)), $product(-1, length1(A, X1))) = 1)) <=> ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, cons(A, X, X1)), $product(-1, length1(A, X1))) = 1)) <=> ![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (^[A: ty] : rewrite(((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length1(A, cons(A, X, X1)) = $sum(1, length1(A, X1)))) <=> ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, cons(A, X, X1)), $product(-1, length1(A, X1))) = 1)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length1(A, cons(A, X, X1)) = $sum(1, length1(A, X1)))) <=> ![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, cons(A, X, X1)), $product(-1, length1(A, X1))) = 1))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length1(A, cons(A, X, X1)) = $sum(1, length1(A, X1)))) <=> ![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length1(A, cons(A, X, X1)) = $sum(1, length1(A, X1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(89,axiom,(![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length1(A, cons(A, X, X1)) = $sum(1, length1(A, X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_def')).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length1(A, cons(A, X, X1)) = $sum(1, length1(A, X1))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, cons(A, X, X1)), $product(-1, length1(A, X1))) = 1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.19/0.44 tff(93,plain,(
% 0.19/0.44 ![A: ty] : ((length1(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))),
% 0.19/0.44 inference(skolemize,[status(sab)],[92])).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[94, 81])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 ((~![A: ty] : (~((~(length1(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(A, X1), $product(-1, length1(A, cons(A, X, X1)))) = -1))))) | (~((~(length1(char1, nil(char1)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(char1, X1), $product(-1, length1(char1, cons(char1, X, X1)))) = -1))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (~((~(length1(char1, nil(char1)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(char1, X1), $product(-1, length1(char1, cons(char1, X, X1)))) = -1)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (((~(length1(char1, nil(char1)) = 0)) | (~![X: uni, X1: uni] : ($sum(length1(char1, X1), $product(-1, length1(char1, cons(char1, X, X1)))) = -1))) | (length1(char1, nil(char1)) = 0)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (length1(char1, nil(char1)) = 0),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 ((~(length1(char1, nil(char1)) = 0)) | $lesseq(length1(char1, nil(char1)), 0)),
% 0.19/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 ($lesseq(length1(char1, nil(char1)), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (^[A: ty, L: uni] : refl($greatereq(length1(A, L), 0) <=> $greatereq(length1(A, L), 0))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (![A: ty, L: uni] : $greatereq(length1(A, L), 0) <=> ![A: ty, L: uni] : $greatereq(length1(A, L), 0)),
% 0.19/0.44 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (^[A: ty, L: uni] : rewrite($lesseq(0, length1(A, L)) <=> $greatereq(length1(A, L), 0))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 (![A: ty, L: uni] : $lesseq(0, length1(A, L)) <=> ![A: ty, L: uni] : $greatereq(length1(A, L), 0)),
% 0.19/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![A: ty, L: uni] : $lesseq(0, length1(A, L)) <=> ![A: ty, L: uni] : $lesseq(0, length1(A, L))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(107,axiom,(![A: ty, L: uni] : $lesseq(0, length1(A, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_nonnegative')).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (![A: ty, L: uni] : $lesseq(0, length1(A, L))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (![A: ty, L: uni] : $greatereq(length1(A, L), 0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.19/0.44 tff(110,plain,(
% 0.19/0.44 ![A: ty, L: uni] : $greatereq(length1(A, L), 0)),
% 0.19/0.44 inference(skolemize,[status(sab)],[109])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (![A: ty, L: uni] : $greatereq(length1(A, L), 0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 ((~![A: ty, L: uni] : $greatereq(length1(A, L), 0)) | $greatereq(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ($greatereq(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(116,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.19/0.44 tff(117,plain,
% 0.19/0.44 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.44 tff(118,plain,(
% 0.19/0.44 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.44 inference(skolemize,[status(sab)],[117])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(nil(char1))) = nil(char1))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (t2tb(tb2t(nil(char1))) = nil(char1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 (((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))))) | (tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(123,plain,
% 0.19/0.45 (tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[122, 59])).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 (tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))) = tb2t(nil(char1))),
% 0.19/0.45 inference(symmetry,[status(thm)],[123])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (t2tb(tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))) = t2tb(tb2t(nil(char1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))) = infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 (t2tb(tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))) = infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[126, 119])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 (infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = t2tb(tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))),
% 0.19/0.45 inference(symmetry,[status(thm)],[127])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 (infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = nil(char1)),
% 0.19/0.45 inference(transitivity,[status(thm)],[128, 125, 121])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))) = length1(char1, nil(char1))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[129])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (length1(char1, nil(char1)) = length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.45 inference(symmetry,[status(thm)],[130])).
% 0.19/0.45 tff(132,plain,
% 0.19/0.45 ((~(length1(char1, nil(char1)) = length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | $greatereq($sum(length1(char1, nil(char1)), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))), 0)),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 ($greatereq($sum(length1(char1, nil(char1)), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (^[A: ty, L1: uni, L2: uni] : refl(($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0) <=> ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(135,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0) <=> ![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (^[A: ty, L1: uni, L2: uni] : trans(monotonicity(rewrite($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = $sum($product(-1, length1(A, L2)), $sum($product(-1, length1(A, L1)), length1(A, infix_plpl(A, L1, L2))))), (($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = 0) <=> ($sum($product(-1, length1(A, L2)), $sum($product(-1, length1(A, L1)), length1(A, infix_plpl(A, L1, L2)))) = 0))), rewrite(($sum($product(-1, length1(A, L2)), $sum($product(-1, length1(A, L1)), length1(A, infix_plpl(A, L1, L2)))) = 0) <=> ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)), (($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = 0) <=> ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : ($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = 0) <=> ![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 (^[A: ty, L1: uni, L2: uni] : rewrite((length1(A, infix_plpl(A, L1, L2)) = $sum(length1(A, L1), length1(A, L2))) <=> ($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = 0))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : (length1(A, infix_plpl(A, L1, L2)) = $sum(length1(A, L1), length1(A, L2))) <=> ![A: ty, L1: uni, L2: uni] : ($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = 0)),
% 0.19/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : (length1(A, infix_plpl(A, L1, L2)) = $sum(length1(A, L1), length1(A, L2))) <=> ![A: ty, L1: uni, L2: uni] : (length1(A, infix_plpl(A, L1, L2)) = $sum(length1(A, L1), length1(A, L2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(141,axiom,(![A: ty, L1: uni, L2: uni] : (length1(A, infix_plpl(A, L1, L2)) = $sum(length1(A, L1), length1(A, L2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','append_length')).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : (length1(A, infix_plpl(A, L1, L2)) = $sum(length1(A, L1), length1(A, L2)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : ($sum(length1(A, infix_plpl(A, L1, L2)), $sum($product(-1, length1(A, L1)), $product(-1, length1(A, L2)))) = 0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[142, 139])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[143, 137])).
% 0.19/0.45 tff(145,plain,(
% 0.19/0.45 ![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)),
% 0.19/0.45 inference(skolemize,[status(sab)],[144])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[145, 135])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 ((~![A: ty, L1: uni, L2: uni] : ($sum(length1(A, L2), $sum(length1(A, L1), $product(-1, length1(A, infix_plpl(A, L1, L2))))) = 0)) | ($sum(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), $sum(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))))) = 0)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ($sum(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), $sum(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))))) = 0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 ((~($sum(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), $sum(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))))) = 0)) | $lesseq($sum(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), $sum(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))))), 0)),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 ($lesseq($sum(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), $sum(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ($lesseq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0) | (~$lesseq(length1(char1, nil(char1)), 0)) | (~$greatereq($sum(length1(char1, nil(char1)), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))), 0)) | (~$greatereq(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)) | (~$lesseq($sum(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), $sum(length1(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))))), $product(-1, length1(char1, infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))))))), 0))),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 ($lesseq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[151, 150, 133, 113, 101])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 ((~![A: ty, L: uni] : $greatereq(length1(A, L), 0)) | $greatereq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 ($greatereq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[153, 111])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 ((length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0) | (~$lesseq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0)) | (~$greatereq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0))),
% 0.19/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 ((length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0) | (~$lesseq(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))), 0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[156, 152])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 ((~((length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0) <=> (t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))) = nil(char1)))) | (~(length1(char1, t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = 0)) | (t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))) = nil(char1))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))) = nil(char1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[158, 157, 76])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (tb2t(t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = tb2t(nil(char1))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 (![I: list_char] : (tb2t(t2tb(I)) = I) <=> ![I: list_char] : (tb2t(t2tb(I)) = I)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (![I: list_char] : (tb2t(t2tb(I)) = I) <=> ![I: list_char] : (tb2t(t2tb(I)) = I)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(163,axiom,(![I: list_char] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (![I: list_char] : (tb2t(t2tb(I)) = I)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.45 tff(165,plain,(
% 0.19/0.45 ![I: list_char] : (tb2t(t2tb(I)) = I)),
% 0.19/0.45 inference(skolemize,[status(sab)],[164])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (![I: list_char] : (tb2t(t2tb(I)) = I)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 ((~![I: list_char] : (tb2t(t2tb(I)) = I)) | (tb2t(t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 (tb2t(t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))))) = tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 (tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))) = tb2t(t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.45 inference(symmetry,[status(thm)],[168])).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 (tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))) = tb2t(nil(char1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[169, 160])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 (mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))) <=> mem2(tb2t(nil(char1)), X1!18)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[170, 67])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 (mem2(tb2t(nil(char1)), X1!18) <=> mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.45 inference(symmetry,[status(thm)],[171])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 ((~mem2(tb2t(nil(char1)), X1!18)) <=> (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (((~(~(Result!17 = true1))) & (~(~mem2(tb2t(nil(char1)), X!19))) & (~((Result1!20 = true1) | mem2(tb2t(nil(char1)), X1!18) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18)))))) <=> ((Result!17 = true1) & mem2(tb2t(nil(char1)), X!19) & (~(mem2(tb2t(nil(char1)), X1!18) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (Result1!20 = true1))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 ((~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | mem2(tb2t(nil(char1)), X1) | (~mem2(tb2t(nil(char1)), concat1(X, X1)))))) <=> (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | mem2(tb2t(nil(char1)), X1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 ((~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | mem2(tb2t(nil(char1)), X1)))) <=> (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | mem2(tb2t(nil(char1)), X1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1))))) <=> (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | mem2(tb2t(nil(char1)), X1))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 ((~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1))))) <=> (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(179,plain,
% 0.19/0.46 ((~![X: regexp1, X1: regexp1, Result: bool1] : (((Result = true1) <=> mem2(tb2t(nil(char1)), X)) => ((Result = true1) => ![Result1: bool1] : (((Result1 = true1) <=> mem2(tb2t(nil(char1)), X1)) => (mem2(tb2t(nil(char1)), concat1(X, X1)) => (Result1 = true1)))))) <=> (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(180,axiom,(~![X: regexp1, X1: regexp1, Result: bool1] : (((Result = true1) <=> mem2(tb2t(nil(char1)), X)) => ((Result = true1) => ![Result1: bool1] : (((Result1 = true1) <=> mem2(tb2t(nil(char1)), X1)) => (mem2(tb2t(nil(char1)), concat1(X, X1)) => (Result1 = true1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_accepts_epsilon')).
% 0.19/0.46 tff(181,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.46 tff(182,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.19/0.46 tff(183,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | ((~(Result = true1)) <=> mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | ((~(Result1 = true1)) <=> mem2(tb2t(nil(char1)), X1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.19/0.46 tff(184,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | (~mem2(tb2t(nil(char1)), concat1(X, X1))) | mem2(tb2t(nil(char1)), X1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[183, 177])).
% 0.19/0.46 tff(185,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | mem2(tb2t(nil(char1)), X1) | (~mem2(tb2t(nil(char1)), concat1(X, X1)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[184, 176])).
% 0.19/0.46 tff(186,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | mem2(tb2t(nil(char1)), X1) | (~mem2(tb2t(nil(char1)), concat1(X, X1)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[185, 175])).
% 0.19/0.46 tff(187,plain,
% 0.19/0.46 (~![X: regexp1, X1: regexp1, Result: bool1] : ((~(Result = true1)) | (~mem2(tb2t(nil(char1)), X)) | ![Result1: bool1] : ((Result1 = true1) | mem2(tb2t(nil(char1)), X1) | (~mem2(tb2t(nil(char1)), concat1(X, X1)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[186, 175])).
% 0.19/0.46 tff(188,plain,
% 0.19/0.46 ((Result!17 = true1) & mem2(tb2t(nil(char1)), X!19) & (~(mem2(tb2t(nil(char1)), X1!18) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (Result1!20 = true1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[187, 174])).
% 0.19/0.46 tff(189,plain,
% 0.19/0.46 (~(mem2(tb2t(nil(char1)), X1!18) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (Result1!20 = true1))),
% 0.19/0.46 inference(and_elim,[status(thm)],[188])).
% 0.19/0.46 tff(190,plain,
% 0.19/0.46 (~mem2(tb2t(nil(char1)), X1!18)),
% 0.19/0.46 inference(or_elim,[status(thm)],[189])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[190, 173])).
% 0.19/0.46 tff(192,plain,
% 0.19/0.46 (((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))))) | mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(193,plain,
% 0.19/0.46 (mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[192, 59])).
% 0.19/0.46 tff(194,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[193, 191])).
% 0.19/0.46 tff(195,plain,((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(196,plain,
% 0.19/0.46 ((concat1(X!19, X1!18) = epsilon1) <=> (epsilon1 = concat1(X!19, X1!18))),
% 0.19/0.46 inference(commutativity,[status(thm)],[])).
% 0.19/0.46 tff(197,plain,
% 0.19/0.46 ((epsilon1 = concat1(X!19, X1!18)) <=> (concat1(X!19, X1!18) = epsilon1)),
% 0.19/0.46 inference(symmetry,[status(thm)],[196])).
% 0.19/0.46 tff(198,plain,
% 0.19/0.46 ((~(epsilon1 = concat1(X!19, X1!18))) <=> (~(concat1(X!19, X1!18) = epsilon1))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.46 tff(199,plain,
% 0.19/0.46 (^[V: regexp1, V1: regexp1] : refl((~(epsilon1 = concat1(V, V1))) <=> (~(epsilon1 = concat1(V, V1))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(200,plain,
% 0.19/0.46 (![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1))) <=> ![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[199])).
% 0.19/0.46 tff(201,plain,
% 0.19/0.46 (![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1))) <=> ![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(202,axiom,(![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','epsilon_Concat')).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 (![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.46 tff(204,plain,(
% 0.19/0.46 ![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[203])).
% 0.19/0.46 tff(205,plain,
% 0.19/0.46 (![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 ((~![V: regexp1, V1: regexp1] : (~(epsilon1 = concat1(V, V1)))) | (~(epsilon1 = concat1(X!19, X1!18)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 (~(epsilon1 = concat1(X!19, X1!18))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (~(concat1(X!19, X1!18) = epsilon1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[207, 198])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 (mem2(tb2t(nil(char1)), concat1(X!19, X1!18))),
% 0.19/0.46 inference(or_elim,[status(thm)],[189])).
% 0.19/0.46 tff(210,plain,
% 0.19/0.46 (^[Z: list_char, Z1: regexp1] : refl(((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z))))))) <=> ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 (![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z))))))) <=> ![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 (^[Z: list_char, Z1: regexp1] : trans(monotonicity(rewrite(((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) <=> (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1))))), rewrite(((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) <=> (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z))))))), rewrite(((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) <=> (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z))))))), rewrite((mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) <=> (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z))))))), rewrite((mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) <=> (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z))))))), rewrite((mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) <=> (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z))))))), rewrite((mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z)))) <=> (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z))))))), ((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (~mem2(Z, Z1)) | ((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z))))) <=> ((~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z))))))))), rewrite(((~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z))))))) <=> ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))), ((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (~mem2(Z, Z1)) | ((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z))))) <=> ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(213,plain,
% 0.19/0.47 (![Z: list_char, Z1: regexp1] : (((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (~mem2(Z, Z1)) | ((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z))))) <=> ![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[212])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (^[Z: list_char, Z1: regexp1] : rewrite((((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z)))) | (~mem2(Z, Z1))) <=> (((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (~mem2(Z, Z1)) | ((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (![Z: list_char, Z1: regexp1] : (((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z)))) | (~mem2(Z, Z1))) <=> ![Z: list_char, Z1: regexp1] : (((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (~mem2(Z, Z1)) | ((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[214])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (![Z: list_char, Z1: regexp1] : (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1))) <=> ![Z: list_char, Z1: regexp1] : (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (^[Z: list_char, Z1: regexp1] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) <=> (((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))))), quant_intro(proof_bind(^[W: list_char, R1: regexp1, R2: regexp1] : rewrite(((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2))) <=> (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))))), (?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2))) <=> ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))))), (((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) <=> ((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2)))))), rewrite(((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2)))) <=> (?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))))), (((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) <=> (?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2)))))), quant_intro(proof_bind(^[W: list_char, R1: regexp1, R2: regexp1] : rewrite(((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2))) <=> (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))))), (?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2))) <=> ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))))), ((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) <=> ((?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2)))))), rewrite(((?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2)))) <=> (?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))))), ((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) <=> (?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2)))))), quant_intro(proof_bind(^[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : trans(monotonicity(rewrite(((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) <=> (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))))), ((((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2))) <=> ((mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2))))), rewrite(((mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2))) <=> (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))), ((((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2))) <=> (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))))), (?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2))) <=> ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))))), (((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) <=> ((?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))))), rewrite(((?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))) <=> (?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))))), (((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) <=> (?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))))), ((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) <=> ((?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))))), rewrite(((?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) <=> (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))))), ((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) <=> (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))))), quant_intro(proof_bind(^[W1: list_char, W2: list_char, R: regexp1] : trans(monotonicity(rewrite(((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) <=> (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))))), ((((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))) <=> ((mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))))), rewrite(((mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))) <=> (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R)))), ((((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))) <=> (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R)))))), (?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))) <=> ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))))), (((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R)))) <=> ((?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R)))))), rewrite(((?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R)))) <=> (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))))), (((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R)))) <=> (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R)))))), ((mem2(Z, Z1) => ((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))))) <=> (mem2(Z, Z1) => (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))))))), rewrite((mem2(Z, Z1) => (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))))) <=> (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1)))), ((mem2(Z, Z1) => ((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))))) <=> (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(218,plain,
% 0.19/0.48 (![Z: list_char, Z1: regexp1] : (mem2(Z, Z1) => ((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R))))) <=> ![Z: list_char, Z1: regexp1] : (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[217])).
% 0.19/0.48 tff(219,axiom,(![Z: list_char, Z1: regexp1] : (mem2(Z, Z1) => ((((((((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R1) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W: list_char, R1: regexp1, R2: regexp1] : ((mem2(W, R2) & (Z = W)) & (Z1 = alt1(R1, R2)))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (((mem2(W1, R1) & mem2(W2, R2)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = concat1(R1, R2)))) | ?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R)))) | ?[W1: list_char, W2: list_char, R: regexp1] : (((mem2(W1, R) & mem2(W2, star1(R))) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2))))) & (Z1 = star1(R)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_inversion')).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (![Z: list_char, Z1: regexp1] : (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 (![Z: list_char, Z1: regexp1] : (?[R: regexp1] : ((Z = tb2t(nil(char1))) & (Z1 = star1(R))) | ?[C: char2] : ((Z = tb2t(cons(char1, t2tb1(C), nil(char1)))) & (Z1 = char3(C))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R1) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W: list_char, R1: regexp1, R2: regexp1] : (mem2(W, R2) & (Z = W) & (Z1 = alt1(R1, R2))) | ?[W1: list_char, W2: list_char, R1: regexp1, R2: regexp1] : (mem2(W1, R1) & mem2(W2, R2) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = concat1(R1, R2))) | ?[W1: list_char, W2: list_char, R: regexp1] : (mem2(W1, R) & mem2(W2, star1(R)) & (Z = tb2t(infix_plpl(char1, t2tb(W1), t2tb(W2)))) & (Z1 = star1(R))) | (~mem2(Z, Z1)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.19/0.48 tff(222,plain,(
% 0.19/0.48 ![Z: list_char, Z1: regexp1] : (((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | ((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z)))) | (~mem2(Z, Z1)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[221])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 (![Z: list_char, Z1: regexp1] : (((Z = tb2t(nil(char1))) & (Z1 = epsilon1)) | (~mem2(Z, Z1)) | ((Z = tb2t(nil(char1))) & (Z1 = star1(tptp_fun_R_2(Z1, Z)))) | ((Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1)))) & (Z1 = char3(tptp_fun_C_3(Z1, Z)))) | (mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z)) & (Z = tptp_fun_W_6(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))) | (mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z)) & (Z = tptp_fun_W_9(Z1, Z)) & (Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))) | (mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z)) & mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z)) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z))))) & (Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))) | (mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z)) & mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z))) & (Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z))))) & (Z1 = star1(tptp_fun_R_14(Z1, Z)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[223, 213])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 (![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[224, 211])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 (((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))) <=> ((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(227,plain,
% 0.19/0.49 (((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))) <=> ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 ((~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(229,plain,
% 0.19/0.49 ((~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 ((~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(231,plain,
% 0.19/0.49 ((~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 ((~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(233,plain,
% 0.19/0.49 ((~(~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))) <=> (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(234,plain,
% 0.19/0.49 (($false | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))) <=> (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(235,plain,
% 0.19/0.49 ((~$true) <=> $false),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(236,plain,
% 0.19/0.49 ((tb2t(nil(char1)) = tb2t(nil(char1))) <=> $true),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(237,plain,
% 0.19/0.49 ((~(tb2t(nil(char1)) = tb2t(nil(char1)))) <=> (~$true)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.49 tff(238,plain,
% 0.19/0.49 ((~(tb2t(nil(char1)) = tb2t(nil(char1)))) <=> $false),
% 0.19/0.49 inference(transitivity,[status(thm)],[237, 235])).
% 0.19/0.49 tff(239,plain,
% 0.19/0.49 (((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))) <=> ($false | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[238])).
% 0.19/0.50 tff(240,plain,
% 0.19/0.50 (((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))) <=> (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[239, 234])).
% 0.19/0.50 tff(241,plain,
% 0.19/0.50 ((~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (~(~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[240])).
% 0.19/0.50 tff(242,plain,
% 0.19/0.50 ((~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) <=> (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[241, 233])).
% 0.19/0.50 tff(243,plain,
% 0.19/0.50 ((~(~(concat1(X!19, X1!18) = epsilon1))) <=> (concat1(X!19, X1!18) = epsilon1)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(244,plain,
% 0.19/0.50 (($false | (~(concat1(X!19, X1!18) = epsilon1))) <=> (~(concat1(X!19, X1!18) = epsilon1))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(245,plain,
% 0.19/0.50 (((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1))) <=> ($false | (~(concat1(X!19, X1!18) = epsilon1)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[238])).
% 0.19/0.50 tff(246,plain,
% 0.19/0.50 (((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1))) <=> (~(concat1(X!19, X1!18) = epsilon1))),
% 0.19/0.50 inference(transitivity,[status(thm)],[245, 244])).
% 0.19/0.50 tff(247,plain,
% 0.19/0.50 ((~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) <=> (~(~(concat1(X!19, X1!18) = epsilon1)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[246])).
% 0.19/0.50 tff(248,plain,
% 0.19/0.50 ((~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) <=> (concat1(X!19, X1!18) = epsilon1)),
% 0.19/0.50 inference(transitivity,[status(thm)],[247, 243])).
% 0.19/0.50 tff(249,plain,
% 0.19/0.50 (((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))) <=> ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[248, 242, 232, 231, 230, 229, 228])).
% 0.19/0.50 tff(250,plain,
% 0.19/0.50 (((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))) <=> ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[249, 227])).
% 0.19/0.50 tff(251,plain,
% 0.19/0.50 (((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))) <=> ((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[250])).
% 0.19/0.50 tff(252,plain,
% 0.19/0.50 (((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))) <=> ((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[251, 226])).
% 0.19/0.51 tff(253,plain,
% 0.19/0.51 ((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | ((~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = epsilon1)))) | (~((~(tb2t(nil(char1)) = tb2t(nil(char1)))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(254,plain,
% 0.19/0.51 ((~![Z: list_char, Z1: regexp1] : ((~mem2(Z, Z1)) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = epsilon1)))) | (~((~(Z = tb2t(nil(char1)))) | (~(Z1 = star1(tptp_fun_R_2(Z1, Z)))))) | (~((~(Z = tb2t(cons(char1, t2tb1(tptp_fun_C_3(Z1, Z)), nil(char1))))) | (~(Z1 = char3(tptp_fun_C_3(Z1, Z)))))) | (~((~mem2(tptp_fun_W_6(Z1, Z), tptp_fun_R1_5(Z1, Z))) | (~(Z = tptp_fun_W_6(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_5(Z1, Z), tptp_fun_R2_4(Z1, Z)))))) | (~((~mem2(tptp_fun_W_9(Z1, Z), tptp_fun_R2_7(Z1, Z))) | (~(Z = tptp_fun_W_9(Z1, Z))) | (~(Z1 = alt1(tptp_fun_R1_8(Z1, Z), tptp_fun_R2_7(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_13(Z1, Z), tptp_fun_R1_11(Z1, Z))) | (~mem2(tptp_fun_W2_12(Z1, Z), tptp_fun_R2_10(Z1, Z))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(Z1, Z)), t2tb(tptp_fun_W2_12(Z1, Z)))))) | (~(Z1 = concat1(tptp_fun_R1_11(Z1, Z), tptp_fun_R2_10(Z1, Z)))))) | (~((~mem2(tptp_fun_W1_16(Z1, Z), tptp_fun_R_14(Z1, Z))) | (~mem2(tptp_fun_W2_15(Z1, Z), star1(tptp_fun_R_14(Z1, Z)))) | (~(Z = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(Z1, Z)), t2tb(tptp_fun_W2_15(Z1, Z)))))) | (~(Z1 = star1(tptp_fun_R_14(Z1, Z)))))))) | (~mem2(tb2t(nil(char1)), concat1(X!19, X1!18))) | (concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.51 tff(255,plain,
% 0.19/0.51 ((concat1(X!19, X1!18) = epsilon1) | (concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[254, 225, 209])).
% 0.19/0.51 tff(256,plain,
% 0.19/0.51 ((concat1(X!19, X1!18) = star1(tptp_fun_R_2(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_13(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_12(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = concat1(tptp_fun_R1_11(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_10(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[255, 208])).
% 0.19/0.51 tff(257,plain,
% 0.19/0.51 ((~((~(tb2t(nil(char1)) = tb2t(cons(char1, t2tb1(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))), nil(char1))))) | (~(concat1(X!19, X1!18) = char3(tptp_fun_C_3(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_6(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_5(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_4(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~((~mem2(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~mem2(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1))), star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1)))))) | (~(tb2t(nil(char1)) = tb2t(infix_plpl(char1, t2tb(tptp_fun_W1_16(concat1(X!19, X1!18), tb2t(nil(char1)))), t2tb(tptp_fun_W2_15(concat1(X!19, X1!18), tb2t(nil(char1)))))))) | (~(concat1(X!19, X1!18) = star1(tptp_fun_R_14(concat1(X!19, X1!18), tb2t(nil(char1))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[256, 195, 49])).
% 0.19/0.52 tff(258,plain,
% 0.19/0.52 (~((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[257, 45, 29, 13])).
% 0.19/0.52 tff(259,plain,
% 0.19/0.52 (((~mem2(tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(tb2t(nil(char1)) = tptp_fun_W_9(concat1(X!19, X1!18), tb2t(nil(char1))))) | (~(concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))))) | (concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(260,plain,
% 0.19/0.52 (concat1(X!19, X1!18) = alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.19/0.52 tff(261,plain,
% 0.19/0.52 (alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)),
% 0.19/0.52 inference(symmetry,[status(thm)],[260])).
% 0.19/0.52 tff(262,plain,
% 0.19/0.52 ((~![U: regexp1, U1: regexp1, V: regexp1, V1: regexp1] : (~(alt1(U, U1) = concat1(V, V1)))) | (~(alt1(tptp_fun_R1_8(concat1(X!19, X1!18), tb2t(nil(char1))), tptp_fun_R2_7(concat1(X!19, X1!18), tb2t(nil(char1)))) = concat1(X!19, X1!18)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(263,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[262, 23, 261])).
% 0.19/0.52 % SZS output end Proof
%------------------------------------------------------------------------------