TSTP Solution File: SWW643_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW643_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:32 EDT 2022
% Result : Theorem 0.22s 0.45s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW643_2 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 20:53:58 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 % SZS output start Proof
% 0.22/0.45 tff(mem_type, type, (
% 0.22/0.45 mem: ( ty * uni * uni ) > $o)).
% 0.22/0.45 tff(nil_type, type, (
% 0.22/0.45 nil: ty > uni)).
% 0.22/0.45 tff(int_type, type, (
% 0.22/0.45 int: ty)).
% 0.22/0.45 tff(t2tb1_type, type, (
% 0.22/0.45 t2tb1: $int > uni)).
% 0.22/0.45 tff(tptp_fun_X_10_type, type, (
% 0.22/0.45 tptp_fun_X_10: $int)).
% 0.22/0.45 tff(t2tb_type, type, (
% 0.22/0.45 t2tb: list_int > uni)).
% 0.22/0.45 tff(tptp_fun_L_9_type, type, (
% 0.22/0.45 tptp_fun_L_9: list_int)).
% 0.22/0.45 tff(tb2t_type, type, (
% 0.22/0.45 tb2t: uni > list_int)).
% 0.22/0.45 tff(true1_type, type, (
% 0.22/0.45 true1: bool1)).
% 0.22/0.45 tff(tptp_fun_Result_15_type, type, (
% 0.22/0.45 tptp_fun_Result_15: bool1)).
% 0.22/0.45 tff(tptp_fun_X2_11_type, type, (
% 0.22/0.45 tptp_fun_X2_11: list_int)).
% 0.22/0.45 tff(sorted1_type, type, (
% 0.22/0.45 sorted1: list_int > $o)).
% 0.22/0.45 tff(tptp_fun_X4_13_type, type, (
% 0.22/0.45 tptp_fun_X4_13: list_int)).
% 0.22/0.45 tff(cons_type, type, (
% 0.22/0.45 cons: ( ty * uni * uni ) > uni)).
% 0.22/0.45 tff(tptp_fun_X3_14_type, type, (
% 0.22/0.45 tptp_fun_X3_14: $int)).
% 0.22/0.45 tff(tptp_fun_X1_12_type, type, (
% 0.22/0.45 tptp_fun_X1_12: $int)).
% 0.22/0.45 tff(tb2t1_type, type, (
% 0.22/0.45 tb2t1: uni > $int)).
% 0.22/0.45 tff(cons_proj_21_type, type, (
% 0.22/0.45 cons_proj_21: ( ty * uni ) > uni)).
% 0.22/0.45 tff(tptp_fun_Y_4_type, type, (
% 0.22/0.45 tptp_fun_Y_4: ( list_int * $int ) > $int)).
% 0.22/0.45 tff(sort1_type, type, (
% 0.22/0.45 sort1: ( ty * uni ) > $o)).
% 0.22/0.45 tff(1,plain,
% 0.22/0.45 (^[I: $int] : refl(($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(2,plain,
% 0.22/0.45 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.45 tff(3,plain,
% 0.22/0.45 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t1(t2tb1(I)), $product(-1, I)) = $sum($product(-1, I), tb2t1(t2tb1(I)))), (($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t1(t2tb1(I))) = 0))), rewrite(($sum($product(-1, I), tb2t1(t2tb1(I))) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)), (($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(4,plain,
% 0.22/0.45 (![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.45 tff(5,plain,
% 0.22/0.45 (^[I: $int] : rewrite((tb2t1(t2tb1(I)) = I) <=> ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(6,plain,
% 0.22/0.45 (![I: $int] : (tb2t1(t2tb1(I)) = I) <=> ![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0)),
% 0.22/0.45 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.45 tff(7,plain,
% 0.22/0.45 (![I: $int] : (tb2t1(t2tb1(I)) = I) <=> ![I: $int] : (tb2t1(t2tb1(I)) = I)),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(8,axiom,(![I: $int] : (tb2t1(t2tb1(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL1')).
% 0.22/0.45 tff(9,plain,
% 0.22/0.45 (![I: $int] : (tb2t1(t2tb1(I)) = I)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.45 tff(10,plain,
% 0.22/0.45 (![I: $int] : ($sum(tb2t1(t2tb1(I)), $product(-1, I)) = 0)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.22/0.45 tff(11,plain,
% 0.22/0.45 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.22/0.45 tff(12,plain,(
% 0.22/0.45 ![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.45 inference(skolemize,[status(sab)],[11])).
% 0.22/0.45 tff(13,plain,
% 0.22/0.45 (![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.22/0.45 tff(14,plain,
% 0.22/0.45 ((~![I: $int] : ($sum(I, $product(-1, tb2t1(t2tb1(I)))) = 0)) | ($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))) = 0)),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(15,plain,
% 0.22/0.45 ($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))) = 0),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.22/0.45 tff(16,plain,
% 0.22/0.45 ((~($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))) = 0)) | $lesseq($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.45 tff(17,plain,
% 0.22/0.45 ($lesseq($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.22/0.45 tff(18,assumption,(~((~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))))))), introduced(assumption)).
% 0.22/0.45 tff(19,plain,
% 0.22/0.45 (((~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))))) | (L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(20,plain,
% 0.22/0.45 (L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.45 tff(21,assumption,(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))), introduced(assumption)).
% 0.22/0.45 tff(22,assumption,(~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))), introduced(assumption)).
% 0.22/0.45 tff(23,plain,
% 0.22/0.45 (($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(24,plain,
% 0.22/0.45 (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 ((~($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))) = 0)) | $greatereq($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 ($greatereq($sum(X1!12, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[25, 15])).
% 0.22/0.45 tff(27,assumption,(~$lesseq($sum(X!10, $product(-1, X1!12)), 0)), introduced(assumption)).
% 0.22/0.45 tff(28,assumption,($lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)), introduced(assumption)).
% 0.22/0.45 tff(29,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(theory_lemma,[status(thm)],[28, 27, 26])).
% 0.22/0.45 tff(30,plain,((~$lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)) | $lesseq($sum(X!10, $product(-1, X1!12)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(31,plain,
% 0.22/0.45 (~$lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[30, 24])).
% 0.22/0.45 tff(32,assumption,(~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))), introduced(assumption)).
% 0.22/0.45 tff(33,plain,
% 0.22/0.45 (((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11)) | (L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(34,plain,
% 0.22/0.45 (L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 (((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11)) | (~(X4!13 = X2!11))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 (~(X4!13 = X2!11)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.22/0.45 tff(37,plain,
% 0.22/0.45 (![I: list_int] : (tb2t(t2tb(I)) = I) <=> ![I: list_int] : (tb2t(t2tb(I)) = I)),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(38,plain,
% 0.22/0.46 (![I: list_int] : (tb2t(t2tb(I)) = I) <=> ![I: list_int] : (tb2t(t2tb(I)) = I)),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(39,axiom,(![I: list_int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 0.22/0.46 tff(40,plain,
% 0.22/0.46 (![I: list_int] : (tb2t(t2tb(I)) = I)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.46 tff(41,plain,(
% 0.22/0.46 ![I: list_int] : (tb2t(t2tb(I)) = I)),
% 0.22/0.46 inference(skolemize,[status(sab)],[40])).
% 0.22/0.46 tff(42,plain,
% 0.22/0.46 (![I: list_int] : (tb2t(t2tb(I)) = I)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.46 tff(43,plain,
% 0.22/0.46 ((~![I: list_int] : (tb2t(t2tb(I)) = I)) | (tb2t(t2tb(X2!11)) = X2!11)),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(44,plain,
% 0.22/0.46 (tb2t(t2tb(X2!11)) = X2!11),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.22/0.46 tff(45,plain,
% 0.22/0.46 (^[A: ty, U: uni, U1: uni] : refl((cons_proj_21(A, cons(A, U, U1)) = U1) <=> (cons_proj_21(A, cons(A, U, U1)) = U1))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(46,plain,
% 0.22/0.46 (![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1) <=> ![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)),
% 0.22/0.46 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.46 tff(47,plain,
% 0.22/0.46 (![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1) <=> ![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(48,axiom,(![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cons_proj_2_def1')).
% 0.22/0.46 tff(49,plain,
% 0.22/0.46 (![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.46 tff(50,plain,(
% 0.22/0.46 ![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)),
% 0.22/0.46 inference(skolemize,[status(sab)],[49])).
% 0.22/0.46 tff(51,plain,
% 0.22/0.46 (![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.22/0.46 tff(52,plain,
% 0.22/0.46 ((~![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)) | (cons_proj_21(int, cons(int, t2tb1(X1!12), t2tb(X2!11))) = t2tb(X2!11))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(53,plain,
% 0.22/0.46 (cons_proj_21(int, cons(int, t2tb1(X1!12), t2tb(X2!11))) = t2tb(X2!11)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.46 tff(54,plain,
% 0.22/0.46 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(55,plain,
% 0.22/0.46 (![J: uni] : (t2tb(tb2t(J)) = J) <=> ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(56,axiom,(![J: uni] : (t2tb(tb2t(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR')).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.22/0.46 tff(58,plain,(
% 0.22/0.46 ![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.22/0.46 inference(skolemize,[status(sab)],[57])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 (![J: uni] : (t2tb(tb2t(J)) = J)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) = cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 (t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) = cons(int, t2tb1(X1!12), t2tb(X2!11))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 (t2tb(L!9) = t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[21])).
% 0.22/0.46 tff(63,assumption,(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13)))), introduced(assumption)).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))) = L!9),
% 0.22/0.46 inference(symmetry,[status(thm)],[63])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (t2tb(tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13)))) = t2tb(L!9)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[64])).
% 0.22/0.46 tff(66,plain,
% 0.22/0.46 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13)))) = cons(int, t2tb1(X3!14), t2tb(X4!13)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(67,plain,
% 0.22/0.46 (t2tb(tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13)))) = cons(int, t2tb1(X3!14), t2tb(X4!13))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[66, 59])).
% 0.22/0.46 tff(68,plain,
% 0.22/0.46 (cons(int, t2tb1(X3!14), t2tb(X4!13)) = t2tb(tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))),
% 0.22/0.46 inference(symmetry,[status(thm)],[67])).
% 0.22/0.46 tff(69,plain,
% 0.22/0.46 (cons(int, t2tb1(X3!14), t2tb(X4!13)) = cons(int, t2tb1(X1!12), t2tb(X2!11))),
% 0.22/0.46 inference(transitivity,[status(thm)],[68, 65, 62, 61])).
% 0.22/0.46 tff(70,plain,
% 0.22/0.46 (cons_proj_21(int, cons(int, t2tb1(X3!14), t2tb(X4!13))) = cons_proj_21(int, cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[69])).
% 0.22/0.46 tff(71,plain,
% 0.22/0.46 ((~![A: ty, U: uni, U1: uni] : (cons_proj_21(A, cons(A, U, U1)) = U1)) | (cons_proj_21(int, cons(int, t2tb1(X3!14), t2tb(X4!13))) = t2tb(X4!13))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(72,plain,
% 0.22/0.46 (cons_proj_21(int, cons(int, t2tb1(X3!14), t2tb(X4!13))) = t2tb(X4!13)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[71, 51])).
% 0.22/0.46 tff(73,plain,
% 0.22/0.46 (t2tb(X4!13) = cons_proj_21(int, cons(int, t2tb1(X3!14), t2tb(X4!13)))),
% 0.22/0.46 inference(symmetry,[status(thm)],[72])).
% 0.22/0.46 tff(74,plain,
% 0.22/0.46 (t2tb(X4!13) = t2tb(X2!11)),
% 0.22/0.46 inference(transitivity,[status(thm)],[73, 70, 53])).
% 0.22/0.46 tff(75,plain,
% 0.22/0.46 (tb2t(t2tb(X4!13)) = tb2t(t2tb(X2!11))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[74])).
% 0.22/0.46 tff(76,plain,
% 0.22/0.46 ((~![I: list_int] : (tb2t(t2tb(I)) = I)) | (tb2t(t2tb(X4!13)) = X4!13)),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(77,plain,
% 0.22/0.46 (tb2t(t2tb(X4!13)) = X4!13),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[76, 42])).
% 0.22/0.46 tff(78,plain,
% 0.22/0.46 (X4!13 = tb2t(t2tb(X4!13))),
% 0.22/0.46 inference(symmetry,[status(thm)],[77])).
% 0.22/0.46 tff(79,plain,
% 0.22/0.46 (X4!13 = X2!11),
% 0.22/0.46 inference(transitivity,[status(thm)],[78, 75, 44])).
% 0.22/0.46 tff(80,assumption,(~(X4!13 = X2!11)), introduced(assumption)).
% 0.22/0.46 tff(81,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.22/0.46 tff(82,plain,((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(83,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[82, 36, 34, 21])).
% 0.22/0.46 tff(84,plain,(((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11)) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(85,plain,
% 0.22/0.46 ((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[84, 21])).
% 0.22/0.46 tff(86,plain,
% 0.22/0.46 (tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))) = L!9),
% 0.22/0.46 inference(symmetry,[status(thm)],[21])).
% 0.22/0.46 tff(87,plain,
% 0.22/0.46 (t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) = t2tb(L!9)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[86])).
% 0.22/0.46 tff(88,plain,
% 0.22/0.46 (t2tb(L!9) = t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.46 inference(symmetry,[status(thm)],[87])).
% 0.22/0.46 tff(89,assumption,(L!9 = tb2t(nil(int))), introduced(assumption)).
% 0.22/0.46 tff(90,plain,
% 0.22/0.46 (t2tb(L!9) = t2tb(tb2t(nil(int)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[89])).
% 0.22/0.46 tff(91,plain,
% 0.22/0.46 (t2tb(tb2t(nil(int))) = t2tb(L!9)),
% 0.22/0.46 inference(symmetry,[status(thm)],[90])).
% 0.22/0.46 tff(92,plain,
% 0.22/0.46 ((~![J: uni] : (t2tb(tb2t(J)) = J)) | (t2tb(tb2t(nil(int))) = nil(int))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(93,plain,
% 0.22/0.46 (t2tb(tb2t(nil(int))) = nil(int)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[92, 59])).
% 0.22/0.46 tff(94,plain,
% 0.22/0.46 (nil(int) = t2tb(tb2t(nil(int)))),
% 0.22/0.46 inference(symmetry,[status(thm)],[93])).
% 0.22/0.46 tff(95,plain,
% 0.22/0.46 (nil(int) = cons(int, t2tb1(X1!12), t2tb(X2!11))),
% 0.22/0.46 inference(transitivity,[status(thm)],[94, 91, 88, 61])).
% 0.22/0.46 tff(96,plain,
% 0.22/0.46 (^[A: ty, V: uni, V1: uni] : refl((~(nil(A) = cons(A, V, V1))) <=> (~(nil(A) = cons(A, V, V1))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(97,plain,
% 0.22/0.46 (![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1))) <=> ![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[96])).
% 0.22/0.46 tff(98,plain,
% 0.22/0.46 (![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1))) <=> ![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(99,axiom,(![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nil_Cons1')).
% 0.22/0.46 tff(100,plain,
% 0.22/0.46 (![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.22/0.46 tff(101,plain,(
% 0.22/0.46 ![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[100])).
% 0.22/0.46 tff(102,plain,
% 0.22/0.46 (![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.22/0.46 tff(103,plain,
% 0.22/0.46 ((~![A: ty, V: uni, V1: uni] : (~(nil(A) = cons(A, V, V1)))) | (~(nil(int) = cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(104,plain,
% 0.22/0.46 (~(nil(int) = cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.22/0.46 tff(105,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[104, 95])).
% 0.22/0.46 tff(106,plain,((~(L!9 = tb2t(nil(int)))) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(107,plain,
% 0.22/0.46 (~(L!9 = tb2t(nil(int)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[106, 21])).
% 0.22/0.46 tff(108,plain,
% 0.22/0.46 (^[X: $int, L: list_int] : refl((~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))) <=> (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(109,plain,
% 0.22/0.46 (![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))) <=> ![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[108])).
% 0.22/0.46 tff(110,plain,
% 0.22/0.46 (^[X: $int, L: list_int] : rewrite((~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))) <=> (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(111,plain,
% 0.22/0.46 (![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))) <=> ![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[110])).
% 0.22/0.46 tff(112,plain,
% 0.22/0.46 (![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))) <=> ![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[111, 109])).
% 0.22/0.46 tff(113,plain,
% 0.22/0.46 (^[X: $int, L: list_int] : trans(monotonicity(rewrite((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) <=> (sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))), rewrite(((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L))) <=> ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))), (((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)))) <=> ((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))))), rewrite(((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0))))))) <=> (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))), (((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)))) <=> (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(114,plain,
% 0.22/0.46 (![X: $int, L: list_int] : ((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)))) <=> ![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[113])).
% 0.22/0.46 tff(115,plain,
% 0.22/0.46 (^[X: $int, L: list_int] : rewrite(((((~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))) | (~sorted1(L))) | sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) & ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)) | (~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))))) <=> ((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(116,plain,
% 0.22/0.46 (![X: $int, L: list_int] : ((((~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))) | (~sorted1(L))) | sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) & ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)) | (~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))))) <=> ![X: $int, L: list_int] : ((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.46 tff(117,plain,
% 0.22/0.46 (^[X: $int, L: list_int] : rewrite(((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) <=> ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(118,plain,
% 0.22/0.46 (![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) <=> ![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[117])).
% 0.22/0.46 tff(119,plain,
% 0.22/0.46 (![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) <=> ![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(120,plain,
% 0.22/0.46 (^[X: $int, L: list_int] : rewrite(((![Y: $int] : (mem(int, t2tb1(Y), t2tb(L)) => $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) <=> ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(121,plain,
% 0.22/0.46 (![X: $int, L: list_int] : ((![Y: $int] : (mem(int, t2tb1(Y), t2tb(L)) => $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) <=> ![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[120])).
% 0.22/0.47 tff(122,axiom,(![X: $int, L: list_int] : ((![Y: $int] : (mem(int, t2tb1(Y), t2tb(L)) => $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sorted_mem')).
% 0.22/0.47 tff(123,plain,
% 0.22/0.47 (![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.22/0.47 tff(124,plain,
% 0.22/0.47 (![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq(X, Y)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.22/0.47 tff(125,plain,
% 0.22/0.47 (![X: $int, L: list_int] : ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)) <=> sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[124, 118])).
% 0.22/0.47 tff(126,plain,(
% 0.22/0.47 ![X: $int, L: list_int] : ((((~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))) | (~sorted1(L))) | sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) & ((![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L)) | (~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[125])).
% 0.22/0.47 tff(127,plain,
% 0.22/0.47 (![X: $int, L: list_int] : ((sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0)))) & ((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)) & sorted1(L))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.22/0.47 tff(128,plain,
% 0.22/0.47 (![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[127, 114])).
% 0.22/0.47 tff(129,plain,
% 0.22/0.47 (![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[128, 112])).
% 0.22/0.47 tff(130,plain,
% 0.22/0.47 (((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))))))))) <=> ((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(131,plain,
% 0.22/0.47 ((~((~(sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~sorted1(X2!11)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, Y)), 0))))))))) <=> (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(132,plain,
% 0.22/0.47 (((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~(sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~sorted1(X2!11)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, Y)), 0)))))))))) <=> ((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[131])).
% 0.22/0.47 tff(133,plain,
% 0.22/0.47 (((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~(sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~sorted1(X2!11)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, Y)), 0)))))))))) <=> ((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[132, 130])).
% 0.22/0.47 tff(134,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~(sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~sorted1(X2!11)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, Y)), 0)))))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(135,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : (~((~(sorted1(tb2t(cons(int, t2tb1(X), t2tb(L)))) | (~sorted1(L)) | (~((~mem(int, t2tb1(tptp_fun_Y_4(L, X)), t2tb(L))) | $lesseq($sum(X, $product(-1, tptp_fun_Y_4(L, X))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X), t2tb(L))))) | (~((~sorted1(L)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(L))) | $lesseq($sum(X, $product(-1, Y)), 0)))))))))) | (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.47 tff(136,plain,
% 0.22/0.47 (~((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[135, 129])).
% 0.22/0.47 tff(137,plain,
% 0.22/0.47 (((~((~sorted1(X2!11)) | sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) | (~((~mem(int, t2tb1(tptp_fun_Y_4(X2!11, X1!12)), t2tb(X2!11))) | $lesseq($sum(X1!12, $product(-1, tptp_fun_Y_4(X2!11, X1!12))), 0))))) | (~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))))))) | ((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(138,plain,
% 0.22/0.47 ((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.22/0.47 tff(139,plain,
% 0.22/0.47 (sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) <=> sorted1(L!9)),
% 0.22/0.47 inference(monotonicity,[status(thm)],[86])).
% 0.22/0.47 tff(140,plain,
% 0.22/0.47 (sorted1(L!9) <=> sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.47 inference(symmetry,[status(thm)],[139])).
% 0.22/0.47 tff(141,plain,
% 0.22/0.47 (((~(~sorted1(L!9))) & ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | ((~(~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))) & ((~((~($sum(X1!12, $product(-1, X!10)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | ((~($sum(X1!12, $product(-1, X!10)) = 0)) & (((~$greatereq($sum(X1!12, $product(-1, X!10)), 0)) & ((~(~(L!9 = tb2t(nil(int))))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))) | (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$greatereq($sum(X1!12, $product(-1, X!10)), 0)))))))))) <=> (sorted1(L!9) & ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | ((L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) & ((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | ((~($sum(X!10, $product(-1, X1!12)) = 0)) & (((~$lesseq($sum(X!10, $product(-1, X1!12)), 0)) & ((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))) | (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(142,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X1, $product(-1, X)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X1, $product(-1, X)) = 0) | (($greatereq($sum(X1, $product(-1, X)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$greatereq($sum(X1, $product(-1, X)), 0)))))))))) <=> (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X1, $product(-1, X)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X1, $product(-1, X)) = 0) | (($greatereq($sum(X1, $product(-1, X)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$greatereq($sum(X1, $product(-1, X)), 0))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(143,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X, $product(-1, X1)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X, $product(-1, X1)) = 0) | (($lesseq($sum(X, $product(-1, X1)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$lesseq($sum(X, $product(-1, X1)), 0)))))))))) <=> (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X1, $product(-1, X)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X1, $product(-1, X)) = 0) | (($greatereq($sum(X1, $product(-1, X)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$greatereq($sum(X1, $product(-1, X)), 0))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(144,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L))))))))))) <=> (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X, $product(-1, X1)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X, $product(-1, X1)) = 0) | (($lesseq($sum(X, $product(-1, X1)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$lesseq($sum(X, $product(-1, X1)), 0))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(145,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L))))))))))) <=> (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L)))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(146,plain,
% 0.22/0.47 ((~![X: $int, L: list_int] : (sorted1(L) => (((L = tb2t(nil(int))) => (~mem(int, t2tb1(X), t2tb(L)))) & ![X1: $int, X2: list_int] : ((L = tb2t(cons(int, t2tb1(X1), t2tb(X2)))) => (((X = X1) => mem(int, t2tb1(X), t2tb(L))) & ((~(X = X1)) => (($less(X1, X) => ((((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((L = tb2t(cons(int, t2tb1(X3), t2tb(X4)))) => (X4 = X2))) & sorted1(X2)) & ![Result: bool1] : (((Result = true1) <=> mem(int, t2tb1(X), t2tb(X2))) => ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$less(X1, X)) => (~mem(int, t2tb1(X), t2tb(L))))))))))) <=> (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L)))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(147,axiom,(~![X: $int, L: list_int] : (sorted1(L) => (((L = tb2t(nil(int))) => (~mem(int, t2tb1(X), t2tb(L)))) & ![X1: $int, X2: list_int] : ((L = tb2t(cons(int, t2tb1(X1), t2tb(X2)))) => (((X = X1) => mem(int, t2tb1(X), t2tb(L))) & ((~(X = X1)) => (($less(X1, X) => ((((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((L = tb2t(cons(int, t2tb1(X3), t2tb(X4)))) => (X4 = X2))) & sorted1(X2)) & ![Result: bool1] : (((Result = true1) <=> mem(int, t2tb1(X), t2tb(X2))) => ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$less(X1, X)) => (~mem(int, t2tb1(X), t2tb(L))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_find')).
% 0.22/0.48 tff(148,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L))))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.22/0.48 tff(149,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L))))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.22/0.48 tff(150,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L))))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.22/0.48 tff(151,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~(X = X1)) | mem(int, t2tb1(X), t2tb(L))) & ((X = X1) | (($lesseq(X, X1) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~$lesseq(X, X1)) | (~mem(int, t2tb1(X), t2tb(L))))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[150, 145])).
% 0.22/0.48 tff(152,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X, $product(-1, X1)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X, $product(-1, X1)) = 0) | (($lesseq($sum(X, $product(-1, X1)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$lesseq($sum(X, $product(-1, X1)), 0)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.22/0.48 tff(153,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X1, $product(-1, X)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X1, $product(-1, X)) = 0) | (($greatereq($sum(X1, $product(-1, X)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$greatereq($sum(X1, $product(-1, X)), 0)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[152, 143])).
% 0.22/0.48 tff(154,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X1, $product(-1, X)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X1, $product(-1, X)) = 0) | (($greatereq($sum(X1, $product(-1, X)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$greatereq($sum(X1, $product(-1, X)), 0)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[153, 142])).
% 0.22/0.48 tff(155,plain,
% 0.22/0.48 (~![X: $int, L: list_int] : ((~sorted1(L)) | (((~mem(int, t2tb1(X), t2tb(L))) | (~(L = tb2t(nil(int))))) & ![X1: $int, X2: list_int] : ((~(L = tb2t(cons(int, t2tb1(X1), t2tb(X2))))) | (((~($sum(X1, $product(-1, X)) = 0)) | mem(int, t2tb1(X), t2tb(L))) & (($sum(X1, $product(-1, X)) = 0) | (($greatereq($sum(X1, $product(-1, X)), 0) | ((~(L = tb2t(nil(int)))) & ![X3: $int, X4: list_int] : ((~(L = tb2t(cons(int, t2tb1(X3), t2tb(X4))))) | (X4 = X2)) & sorted1(X2) & ![Result: bool1] : (((~(Result = true1)) <=> mem(int, t2tb1(X), t2tb(X2))) | ((Result = true1) <=> mem(int, t2tb1(X), t2tb(L)))))) & ((~mem(int, t2tb1(X), t2tb(L))) | (~$greatereq($sum(X1, $product(-1, X)), 0)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[154, 142])).
% 0.22/0.48 tff(156,plain,
% 0.22/0.48 (sorted1(L!9) & ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | ((L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) & ((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | ((~($sum(X!10, $product(-1, X1!12)) = 0)) & (((~$lesseq($sum(X!10, $product(-1, X1!12)), 0)) & ((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))) | (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[155, 141])).
% 0.22/0.48 tff(157,plain,
% 0.22/0.48 (sorted1(L!9)),
% 0.22/0.48 inference(and_elim,[status(thm)],[156])).
% 0.22/0.48 tff(158,plain,
% 0.22/0.48 (sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[157, 140])).
% 0.22/0.48 tff(159,plain,
% 0.22/0.48 ((~((~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))))) | (~sorted1(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(160,plain,
% 0.22/0.48 (~((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[159, 158, 138])).
% 0.22/0.48 tff(161,plain,
% 0.22/0.48 (((~sorted1(X2!11)) | (~![Y: $int] : ((~mem(int, t2tb1(Y), t2tb(X2!11))) | $greatereq($sum(Y, $product(-1, X1!12)), 0)))) | sorted1(X2!11)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(162,plain,
% 0.22/0.48 (sorted1(X2!11)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.22/0.48 tff(163,plain,
% 0.22/0.48 (($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))) | ((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(164,plain,
% 0.22/0.48 ((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[163, 22])).
% 0.22/0.48 tff(165,plain,
% 0.22/0.48 ((~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))) | (L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(166,plain,
% 0.22/0.48 (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[165, 164, 162, 107, 85])).
% 0.22/0.48 tff(167,plain,
% 0.22/0.48 ((((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))) | (~((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(168,plain,
% 0.22/0.48 (~((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.22/0.48 tff(169,plain,
% 0.22/0.48 ((((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))) | (~((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(170,plain,
% 0.22/0.48 (~((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[169, 166])).
% 0.22/0.48 tff(171,plain,
% 0.22/0.48 (t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) = t2tb(L!9)),
% 0.22/0.48 inference(symmetry,[status(thm)],[62])).
% 0.22/0.48 tff(172,plain,
% 0.22/0.48 (cons(int, t2tb1(X1!12), t2tb(X2!11)) = t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.48 inference(symmetry,[status(thm)],[61])).
% 0.22/0.48 tff(173,plain,
% 0.22/0.48 (cons(int, t2tb1(X1!12), t2tb(X2!11)) = t2tb(L!9)),
% 0.22/0.48 inference(transitivity,[status(thm)],[172, 171])).
% 0.22/0.48 tff(174,plain,
% 0.22/0.48 (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[173])).
% 0.22/0.48 tff(175,plain,
% 0.22/0.48 (mem(int, t2tb1(X!10), t2tb(L!9)) <=> mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.48 inference(symmetry,[status(thm)],[174])).
% 0.22/0.48 tff(176,plain,
% 0.22/0.48 ((~mem(int, t2tb1(X!10), t2tb(L!9))) <=> (~mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[175])).
% 0.22/0.48 tff(177,assumption,(~((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))), introduced(assumption)).
% 0.22/0.48 tff(178,assumption,(~((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11)))), introduced(assumption)).
% 0.22/0.48 tff(179,plain,
% 0.22/0.48 ((t2tb1(X!10) = t2tb1(X1!12)) <=> (t2tb1(X1!12) = t2tb1(X!10))),
% 0.22/0.48 inference(commutativity,[status(thm)],[])).
% 0.22/0.48 tff(180,plain,
% 0.22/0.48 ((t2tb1(X1!12) = t2tb1(X!10)) <=> (t2tb1(X!10) = t2tb1(X1!12))),
% 0.22/0.48 inference(symmetry,[status(thm)],[179])).
% 0.22/0.48 tff(181,plain,
% 0.22/0.48 ((~(t2tb1(X1!12) = t2tb1(X!10))) <=> (~(t2tb1(X!10) = t2tb1(X1!12)))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[180])).
% 0.22/0.48 tff(182,plain,
% 0.22/0.48 (^[X: $int] : refl(sort1(int, t2tb1(X)) <=> sort1(int, t2tb1(X)))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(183,plain,
% 0.22/0.48 (![X: $int] : sort1(int, t2tb1(X)) <=> ![X: $int] : sort1(int, t2tb1(X))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[182])).
% 0.22/0.48 tff(184,plain,
% 0.22/0.48 (![X: $int] : sort1(int, t2tb1(X)) <=> ![X: $int] : sort1(int, t2tb1(X))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(185,axiom,(![X: $int] : sort1(int, t2tb1(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort1')).
% 0.22/0.48 tff(186,plain,
% 0.22/0.48 (![X: $int] : sort1(int, t2tb1(X))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.22/0.48 tff(187,plain,(
% 0.22/0.48 ![X: $int] : sort1(int, t2tb1(X))),
% 0.22/0.48 inference(skolemize,[status(sab)],[186])).
% 0.22/0.48 tff(188,plain,
% 0.22/0.48 (![X: $int] : sort1(int, t2tb1(X))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.22/0.48 tff(189,plain,
% 0.22/0.48 ((~![X: $int] : sort1(int, t2tb1(X))) | sort1(int, t2tb1(X!10))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(190,plain,
% 0.22/0.48 (sort1(int, t2tb1(X!10))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.22/0.48 tff(191,plain,
% 0.22/0.48 ((~![X: $int] : sort1(int, t2tb1(X))) | sort1(int, t2tb1(X1!12))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(192,plain,
% 0.22/0.48 (sort1(int, t2tb1(X1!12))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.22/0.48 tff(193,plain,
% 0.22/0.48 (^[A: ty, X: uni] : refl(((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))) <=> ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(194,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))) <=> ![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[193])).
% 0.22/0.48 tff(195,plain,
% 0.22/0.48 (^[A: ty, X: uni] : rewrite(((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))) <=> ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(196,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))) <=> ![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[195])).
% 0.22/0.48 tff(197,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))) <=> ![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[196, 194])).
% 0.22/0.48 tff(198,plain,
% 0.22/0.48 (^[A: ty, X: uni] : rewrite(((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(199,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> ![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[198])).
% 0.22/0.48 tff(200,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> ![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(201,plain,
% 0.22/0.48 (^[A: ty, X: uni] : trans(monotonicity(rewrite(((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : (sort1(A, X1) => (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))) <=> ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))), ((sort1(A, X) => ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : (sort1(A, X1) => (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> (sort1(A, X) => ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))))), rewrite((sort1(A, X) => ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))), ((sort1(A, X) => ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : (sort1(A, X1) => (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(202,plain,
% 0.22/0.48 (![A: ty, X: uni] : (sort1(A, X) => ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : (sort1(A, X1) => (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2)))))) <=> ![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[201])).
% 0.22/0.48 tff(203,axiom,(![A: ty, X: uni] : (sort1(A, X) => ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : (sort1(A, X1) => (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mem_def')).
% 0.22/0.48 tff(204,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.22/0.48 tff(205,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.22/0.48 tff(206,plain,(
% 0.22/0.48 ![A: ty, X: uni] : ((~sort1(A, X)) | ((~mem(A, X, nil(A))) & ![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[205])).
% 0.22/0.48 tff(207,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.22/0.48 tff(208,plain,
% 0.22/0.48 (![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[207, 197])).
% 0.22/0.48 tff(209,plain,
% 0.22/0.48 (((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | ((~sort1(int, t2tb1(X1!12))) | (~(mem(int, t2tb1(X1!12), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))))))) <=> ((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | (~sort1(int, t2tb1(X1!12))) | (~(mem(int, t2tb1(X1!12), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(210,plain,
% 0.22/0.48 ((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | ((~sort1(int, t2tb1(X1!12))) | (~(mem(int, t2tb1(X1!12), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(211,plain,
% 0.22/0.48 ((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | (~sort1(int, t2tb1(X1!12))) | (~(mem(int, t2tb1(X1!12), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.22/0.48 tff(212,plain,
% 0.22/0.48 (~(mem(int, t2tb1(X1!12), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[211, 208, 192])).
% 0.22/0.48 tff(213,plain,
% 0.22/0.48 ((mem(int, t2tb1(X1!12), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2)))))) | ![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(214,plain,
% 0.22/0.48 (![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.22/0.48 tff(215,plain,
% 0.22/0.48 (((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X!10))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) <=> ((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int)))))) <=> ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | (~sort1(int, t2tb1(X!10))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) <=> ((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(216,plain,
% 0.22/0.48 ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X!10))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) <=> ((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(217,plain,
% 0.22/0.48 ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | (~sort1(int, t2tb1(X!10))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) <=> ((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.22/0.48 tff(218,plain,
% 0.22/0.48 (mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) <=> ((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[217, 214, 190])).
% 0.22/0.48 tff(219,plain,
% 0.22/0.48 (cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))) = cons(int, t2tb1(X!10), nil(int))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[93])).
% 0.22/0.48 tff(220,plain,
% 0.22/0.48 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(221,plain,
% 0.22/0.48 (![J: uni] : (t2tb1(tb2t1(J)) = J) <=> ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(222,axiom,(![J: uni] : (t2tb1(tb2t1(J)) = J)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeR1')).
% 0.22/0.48 tff(223,plain,
% 0.22/0.48 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.22/0.49 tff(224,plain,(
% 0.22/0.49 ![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.49 inference(skolemize,[status(sab)],[223])).
% 0.22/0.49 tff(225,plain,
% 0.22/0.49 (![J: uni] : (t2tb1(tb2t1(J)) = J)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.22/0.49 tff(226,plain,
% 0.22/0.49 ((~![J: uni] : (t2tb1(tb2t1(J)) = J)) | (t2tb1(tb2t1(t2tb1(X1!12))) = t2tb1(X1!12))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(227,plain,
% 0.22/0.49 (t2tb1(tb2t1(t2tb1(X1!12))) = t2tb1(X1!12)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.22/0.49 tff(228,plain,
% 0.22/0.49 (mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))) <=> mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[227, 219])).
% 0.22/0.49 tff(229,plain,
% 0.22/0.49 ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) <=> (~mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[228])).
% 0.22/0.49 tff(230,plain,
% 0.22/0.49 (tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))) = tb2t(cons(int, t2tb1(X!10), nil(int)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[219])).
% 0.22/0.49 tff(231,plain,
% 0.22/0.49 (sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) <=> sorted1(tb2t(cons(int, t2tb1(X!10), nil(int))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[230])).
% 0.22/0.49 tff(232,plain,
% 0.22/0.49 (sorted1(tb2t(cons(int, t2tb1(X!10), nil(int)))) <=> sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))),
% 0.22/0.49 inference(symmetry,[status(thm)],[231])).
% 0.22/0.49 tff(233,plain,
% 0.22/0.49 (^[X: $int] : refl(sorted1(tb2t(cons(int, t2tb1(X), nil(int)))) <=> sorted1(tb2t(cons(int, t2tb1(X), nil(int)))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(234,plain,
% 0.22/0.49 (![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int)))) <=> ![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[233])).
% 0.22/0.49 tff(235,plain,
% 0.22/0.49 (![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int)))) <=> ![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(236,axiom,(![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sorted_One')).
% 0.22/0.49 tff(237,plain,
% 0.22/0.49 (![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.22/0.49 tff(238,plain,(
% 0.22/0.49 ![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[237])).
% 0.22/0.49 tff(239,plain,
% 0.22/0.49 (![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.22/0.49 tff(240,plain,
% 0.22/0.49 ((~![X: $int] : sorted1(tb2t(cons(int, t2tb1(X), nil(int))))) | sorted1(tb2t(cons(int, t2tb1(X!10), nil(int))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(241,plain,
% 0.22/0.49 (sorted1(tb2t(cons(int, t2tb1(X!10), nil(int))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.22/0.49 tff(242,plain,
% 0.22/0.49 (sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[241, 232])).
% 0.22/0.49 tff(243,assumption,(~$lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)), introduced(assumption)).
% 0.22/0.49 tff(244,plain,
% 0.22/0.49 (^[X: $int, Y: $int, L: list_int] : refl(((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0)) <=> ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(245,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0)) <=> ![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[244])).
% 0.22/0.49 tff(246,plain,
% 0.22/0.49 (^[X: $int, Y: $int, L: list_int] : rewrite(((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq($sum(Y, $product(-1, X)), 0)) <=> ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(247,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq($sum(Y, $product(-1, X)), 0)) <=> ![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[246])).
% 0.22/0.49 tff(248,plain,
% 0.22/0.49 (^[X: $int, Y: $int, L: list_int] : rewrite(((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X)) <=> ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq($sum(Y, $product(-1, X)), 0)))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(249,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X)) <=> ![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq($sum(Y, $product(-1, X)), 0))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[248])).
% 0.22/0.49 tff(250,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X)) <=> ![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(251,plain,
% 0.22/0.49 (^[X: $int, Y: $int, L: list_int] : trans(monotonicity(rewrite($less(X, Y) <=> (~$lesseq(Y, X))), rewrite((sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L)))) => (~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L))))) <=> ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))))), (($less(X, Y) => (sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L)))) => (~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))))) <=> ((~$lesseq(Y, X)) => ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))))))), rewrite(((~$lesseq(Y, X)) => ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))))) <=> ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X))), (($less(X, Y) => (sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L)))) => (~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))))) <=> ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(252,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ($less(X, Y) => (sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L)))) => (~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))))) <=> ![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[251])).
% 0.22/0.49 tff(253,axiom,(![X: $int, Y: $int, L: list_int] : ($less(X, Y) => (sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L)))) => (~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sorted_not_mem')).
% 0.22/0.49 tff(254,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.22/0.49 tff(255,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq(Y, X))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.22/0.49 tff(256,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $lesseq($sum(Y, $product(-1, X)), 0))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[255, 249])).
% 0.22/0.49 tff(257,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[256, 247])).
% 0.22/0.49 tff(258,plain,(
% 0.22/0.49 ![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.22/0.49 inference(skolemize,[status(sab)],[257])).
% 0.22/0.49 tff(259,plain,
% 0.22/0.49 (![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[258, 245])).
% 0.22/0.49 tff(260,plain,
% 0.22/0.49 (((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))) <=> ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(261,plain,
% 0.22/0.49 (((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $greatereq($sum(tb2t1(t2tb1(X1!12)), $product(-1, X!10)), 0)) <=> ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(262,plain,
% 0.22/0.49 (((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $greatereq($sum(tb2t1(t2tb1(X1!12)), $product(-1, X!10)), 0))) <=> ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[261])).
% 0.22/0.49 tff(263,plain,
% 0.22/0.49 (((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $greatereq($sum(tb2t1(t2tb1(X1!12)), $product(-1, X!10)), 0))) <=> ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))),
% 0.22/0.49 inference(transitivity,[status(thm)],[262, 260])).
% 0.22/0.49 tff(264,plain,
% 0.22/0.49 ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $greatereq($sum(tb2t1(t2tb1(X1!12)), $product(-1, X!10)), 0))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(265,plain,
% 0.22/0.49 ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))) | (~sorted1(tb2t(cons(int, t2tb1(X!10), t2tb(tb2t(nil(int))))))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.22/0.49 tff(266,plain,
% 0.22/0.49 (~mem(int, t2tb1(tb2t1(t2tb1(X1!12))), cons(int, t2tb1(X!10), t2tb(tb2t(nil(int)))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[265, 259, 243, 242])).
% 0.22/0.49 tff(267,plain,
% 0.22/0.49 (~mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[266, 229])).
% 0.22/0.49 tff(268,plain,
% 0.22/0.49 ((~(mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) <=> ((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int))))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X!10), nil(int))) | (~((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(269,plain,
% 0.22/0.49 (~((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[268, 267, 218])).
% 0.22/0.49 tff(270,plain,
% 0.22/0.49 (((t2tb1(X1!12) = t2tb1(X!10)) | mem(int, t2tb1(X1!12), nil(int))) | (~(t2tb1(X1!12) = t2tb1(X!10)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(271,plain,
% 0.22/0.49 (~(t2tb1(X1!12) = t2tb1(X!10))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[270, 269])).
% 0.22/0.49 tff(272,plain,
% 0.22/0.49 (~(t2tb1(X!10) = t2tb1(X1!12))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[271, 181])).
% 0.22/0.49 tff(273,assumption,(~mem(int, t2tb1(X!10), t2tb(X2!11))), introduced(assumption)).
% 0.22/0.49 tff(274,plain,
% 0.22/0.49 (((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | (~(Result!15 = true1)) | mem(int, t2tb1(X!10), t2tb(X2!11))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(275,plain,
% 0.22/0.49 (~(Result!15 = true1)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[274, 273, 178])).
% 0.22/0.49 tff(276,plain,
% 0.22/0.49 (((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))) | (Result!15 = true1) | mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(277,plain,
% 0.22/0.49 (mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[276, 275, 177])).
% 0.22/0.49 tff(278,plain,
% 0.22/0.49 (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[277, 175])).
% 0.22/0.49 tff(279,plain,
% 0.22/0.49 (((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | ((~sort1(int, t2tb1(X!10))) | (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))))))) <=> ((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | (~sort1(int, t2tb1(X!10))) | (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(280,plain,
% 0.22/0.49 ((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | ((~sort1(int, t2tb1(X!10))) | (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(281,plain,
% 0.22/0.49 ((~![A: ty, X: uni] : ((~sort1(A, X)) | (~(mem(A, X, nil(A)) | (~![X1: uni, X2: uni] : ((~sort1(A, X1)) | (mem(A, X, cons(A, X1, X2)) <=> ((X = X1) | mem(A, X, X2))))))))) | (~sort1(int, t2tb1(X!10))) | (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2)))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.22/0.49 tff(282,plain,
% 0.22/0.49 (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[281, 208, 190])).
% 0.22/0.49 tff(283,plain,
% 0.22/0.49 ((mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2)))))) | ![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(284,plain,
% 0.22/0.49 (![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.22/0.49 tff(285,plain,
% 0.22/0.49 (((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))) | ((~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))))) <=> ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))) | (~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(286,plain,
% 0.22/0.49 ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))) | ((~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(287,plain,
% 0.22/0.49 ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))) | (~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.22/0.49 tff(288,plain,
% 0.22/0.49 (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[287, 192, 284])).
% 0.22/0.49 tff(289,assumption,(~(t2tb1(X!10) = t2tb1(X1!12))), introduced(assumption)).
% 0.22/0.49 tff(290,plain,
% 0.22/0.49 ((~((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))) | (t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(291,plain,
% 0.22/0.49 (~((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[290, 273, 289])).
% 0.22/0.49 tff(292,plain,
% 0.22/0.49 ((~(mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))))) | (~mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11)))) | ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(293,plain,
% 0.22/0.49 (~mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[292, 291, 288])).
% 0.22/0.49 tff(294,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[293, 278])).
% 0.22/0.50 tff(295,plain,(mem(int, t2tb1(X!10), t2tb(X2!11)) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))) | (t2tb1(X!10) = t2tb1(X1!12)) | ((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(296,plain,
% 0.22/0.50 (mem(int, t2tb1(X!10), t2tb(X2!11))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[295, 272, 177, 21, 178])).
% 0.22/0.50 tff(297,plain,
% 0.22/0.50 (((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | (Result!15 = true1) | (~mem(int, t2tb1(X!10), t2tb(X2!11)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(298,plain,
% 0.22/0.50 (Result!15 = true1),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[297, 296, 178])).
% 0.22/0.50 tff(299,plain,
% 0.22/0.50 (((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))) | (~(Result!15 = true1)) | (~mem(int, t2tb1(X!10), t2tb(L!9)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(300,plain,
% 0.22/0.50 (~mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[299, 298, 177])).
% 0.22/0.50 tff(301,plain,
% 0.22/0.50 (~mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[300, 176])).
% 0.22/0.50 tff(302,plain,
% 0.22/0.50 (((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))) | (~mem(int, t2tb1(X!10), t2tb(X2!11)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(303,plain,
% 0.22/0.50 ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[302, 296])).
% 0.22/0.50 tff(304,plain,
% 0.22/0.50 ((~(mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))))) | mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11))) | (~((t2tb1(X!10) = t2tb1(X1!12)) | mem(int, t2tb1(X!10), t2tb(X2!11))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(305,plain,
% 0.22/0.50 (mem(int, t2tb1(X!10), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[304, 303, 288])).
% 0.22/0.50 tff(306,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[305, 301])).
% 0.22/0.50 tff(307,plain,(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))) | $lesseq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(308,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[307, 170, 168, 31, 21])).
% 0.22/0.50 tff(309,plain,(($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(310,plain,
% 0.22/0.50 ($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[309, 20])).
% 0.22/0.50 tff(311,plain,
% 0.22/0.50 (((~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))))) | ((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(312,plain,
% 0.22/0.50 ((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[311, 18])).
% 0.22/0.50 tff(313,assumption,($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))), introduced(assumption)).
% 0.22/0.50 tff(314,plain,
% 0.22/0.50 (((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))) | $lesseq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(315,plain,
% 0.22/0.50 ((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[314, 27])).
% 0.22/0.50 tff(316,plain,
% 0.22/0.50 ((~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))) | (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(317,plain,
% 0.22/0.50 (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[316, 315, 313])).
% 0.22/0.50 tff(318,assumption,((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))), introduced(assumption)).
% 0.22/0.50 tff(319,plain,
% 0.22/0.50 ((~($sum(X!10, $product(-1, X1!12)) = 0)) | $lesseq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.50 tff(320,plain,
% 0.22/0.50 (~($sum(X!10, $product(-1, X1!12)) = 0)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[319, 27])).
% 0.22/0.50 tff(321,plain,
% 0.22/0.50 (((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9))) | ($sum(X!10, $product(-1, X1!12)) = 0)),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(322,plain,
% 0.22/0.50 ((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.22/0.50 tff(323,plain,
% 0.22/0.50 ((~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))))) | (~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(324,plain,
% 0.22/0.50 (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[323, 322, 318])).
% 0.22/0.50 tff(325,plain,
% 0.22/0.50 ((($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))) | ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(326,plain,
% 0.22/0.50 ($false),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[325, 324, 317])).
% 0.22/0.50 tff(327,plain,($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.50 tff(328,plain,
% 0.22/0.50 ($lesseq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[327, 312, 310])).
% 0.22/0.50 tff(329,assumption,(~mem(int, t2tb1(X!10), t2tb(L!9))), introduced(assumption)).
% 0.22/0.50 tff(330,plain,
% 0.22/0.50 (X1!12 = tb2t1(t2tb1(X1!12))),
% 0.22/0.50 inference(theory_lemma,[status(thm)],[26, 17])).
% 0.22/0.50 tff(331,assumption,($sum(X!10, $product(-1, X1!12)) = 0), introduced(assumption)).
% 0.22/0.50 tff(332,plain,
% 0.22/0.50 ($lesseq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[319, 331])).
% 0.22/0.50 tff(333,plain,
% 0.22/0.50 ((~($sum(X!10, $product(-1, X1!12)) = 0)) | $greatereq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.50 tff(334,plain,
% 0.22/0.50 ($greatereq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[333, 331])).
% 0.22/0.50 tff(335,plain,
% 0.22/0.50 (X!10 = X1!12),
% 0.22/0.50 inference(theory_lemma,[status(thm)],[334, 332])).
% 0.22/0.50 tff(336,plain,
% 0.22/0.50 (X!10 = tb2t1(t2tb1(X1!12))),
% 0.22/0.50 inference(transitivity,[status(thm)],[335, 330])).
% 0.22/0.50 tff(337,plain,
% 0.22/0.50 (t2tb1(X!10) = t2tb1(tb2t1(t2tb1(X1!12)))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.50 tff(338,plain,
% 0.22/0.50 (t2tb1(tb2t1(t2tb1(X1!12))) = t2tb1(X!10)),
% 0.22/0.50 inference(symmetry,[status(thm)],[337])).
% 0.22/0.50 tff(339,plain,
% 0.22/0.50 (t2tb1(X1!12) = t2tb1(tb2t1(t2tb1(X1!12)))),
% 0.22/0.50 inference(symmetry,[status(thm)],[227])).
% 0.22/0.50 tff(340,plain,
% 0.22/0.50 (t2tb1(X1!12) = t2tb1(X!10)),
% 0.22/0.50 inference(transitivity,[status(thm)],[339, 338])).
% 0.22/0.50 tff(341,plain,
% 0.22/0.50 (mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[340, 173])).
% 0.22/0.50 tff(342,plain,
% 0.22/0.50 (mem(int, t2tb1(X!10), t2tb(L!9)) <=> mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.50 inference(symmetry,[status(thm)],[341])).
% 0.22/0.50 tff(343,plain,
% 0.22/0.50 ((~mem(int, t2tb1(X!10), t2tb(L!9))) <=> (~mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[342])).
% 0.22/0.50 tff(344,plain,
% 0.22/0.50 (~mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[329, 343])).
% 0.22/0.50 tff(345,plain,
% 0.22/0.50 (((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X1!12))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))))) <=> ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | (~sort1(int, t2tb1(X1!12))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(346,plain,
% 0.22/0.50 (((~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X1!12) = t2tb1(X1!12)) | mem(int, t2tb1(X1!12), t2tb(X2!11))))) <=> ((~sort1(int, t2tb1(X1!12))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(347,plain,
% 0.22/0.50 (((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X1!12) = t2tb1(X1!12)) | mem(int, t2tb1(X1!12), t2tb(X2!11)))))) <=> ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X1!12))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11)))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[346])).
% 0.22/0.50 tff(348,plain,
% 0.22/0.50 (((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X1!12) = t2tb1(X1!12)) | mem(int, t2tb1(X1!12), t2tb(X2!11)))))) <=> ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | (~sort1(int, t2tb1(X1!12))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[347, 345])).
% 0.22/0.50 tff(349,plain,
% 0.22/0.50 ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | ((~sort1(int, t2tb1(X1!12))) | (mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11))) <=> ((t2tb1(X1!12) = t2tb1(X1!12)) | mem(int, t2tb1(X1!12), t2tb(X2!11)))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(350,plain,
% 0.22/0.51 ((~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X1!12), cons(int, X1, X2)) <=> ((t2tb1(X1!12) = X1) | mem(int, t2tb1(X1!12), X2))))) | (~sort1(int, t2tb1(X1!12))) | mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.22/0.51 tff(351,plain,
% 0.22/0.51 (mem(int, t2tb1(X1!12), cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[350, 192, 214])).
% 0.22/0.51 tff(352,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[351, 344])).
% 0.22/0.51 tff(353,plain,((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(354,plain,
% 0.22/0.51 (~($sum(X!10, $product(-1, X1!12)) = 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[353, 329, 21])).
% 0.22/0.51 tff(355,plain,
% 0.22/0.51 ((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[321, 354])).
% 0.22/0.51 tff(356,plain,
% 0.22/0.51 ($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[309, 21])).
% 0.22/0.51 tff(357,plain,
% 0.22/0.51 (((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))) | mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(358,plain,
% 0.22/0.51 ((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[357, 329])).
% 0.22/0.51 tff(359,plain,
% 0.22/0.51 (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[316, 358, 356])).
% 0.22/0.51 tff(360,plain,
% 0.22/0.51 (($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[325, 359])).
% 0.22/0.51 tff(361,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[323, 360, 355, 318])).
% 0.22/0.51 tff(362,plain,(mem(int, t2tb1(X!10), t2tb(L!9)) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))))) | (~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(363,plain,
% 0.22/0.51 (mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[362, 312, 20])).
% 0.22/0.51 tff(364,plain,
% 0.22/0.51 (((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9))) | (~mem(int, t2tb1(X!10), t2tb(L!9)))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(365,plain,
% 0.22/0.51 ((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[364, 363])).
% 0.22/0.51 tff(366,plain,
% 0.22/0.51 (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[323, 365, 312])).
% 0.22/0.51 tff(367,plain,
% 0.22/0.51 ((($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))) | (~($sum(X!10, $product(-1, X1!12)) = 0))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(368,plain,
% 0.22/0.51 (~($sum(X!10, $product(-1, X1!12)) = 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[367, 366])).
% 0.22/0.51 tff(369,plain,
% 0.22/0.51 (($sum(X!10, $product(-1, X1!12)) = 0) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)) | (~$greatereq($sum(X!10, $product(-1, X1!12)), 0))),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.22/0.51 tff(370,plain,
% 0.22/0.51 (~$greatereq($sum(X!10, $product(-1, X1!12)), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[369, 368, 328])).
% 0.22/0.51 tff(371,plain,
% 0.22/0.51 (t2tb(L!9) = t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[20])).
% 0.22/0.51 tff(372,plain,
% 0.22/0.51 (t2tb(tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) = t2tb(L!9)),
% 0.22/0.51 inference(symmetry,[status(thm)],[371])).
% 0.22/0.51 tff(373,plain,
% 0.22/0.51 (cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)) = cons(int, t2tb1(X1!12), t2tb(X2!11))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[227])).
% 0.22/0.51 tff(374,plain,
% 0.22/0.51 (cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)) = t2tb(L!9)),
% 0.22/0.51 inference(transitivity,[status(thm)],[373, 172, 372])).
% 0.22/0.51 tff(375,plain,
% 0.22/0.51 (mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))) <=> mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[374])).
% 0.22/0.51 tff(376,plain,
% 0.22/0.51 (mem(int, t2tb1(X!10), t2tb(L!9)) <=> mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))),
% 0.22/0.51 inference(symmetry,[status(thm)],[375])).
% 0.22/0.51 tff(377,plain,
% 0.22/0.51 (mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[363, 376])).
% 0.22/0.51 tff(378,plain,
% 0.22/0.51 (tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))) = L!9),
% 0.22/0.51 inference(symmetry,[status(thm)],[20])).
% 0.22/0.51 tff(379,plain,
% 0.22/0.51 (tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))) = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[373])).
% 0.22/0.51 tff(380,plain,
% 0.22/0.51 (tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))) = L!9),
% 0.22/0.51 inference(transitivity,[status(thm)],[379, 378])).
% 0.22/0.51 tff(381,plain,
% 0.22/0.51 (sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))) <=> sorted1(L!9)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[380])).
% 0.22/0.51 tff(382,plain,
% 0.22/0.51 (sorted1(L!9) <=> sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))))),
% 0.22/0.51 inference(symmetry,[status(thm)],[381])).
% 0.22/0.51 tff(383,plain,
% 0.22/0.51 (sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[157, 382])).
% 0.22/0.51 tff(384,plain,
% 0.22/0.51 (((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))) | (~sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))))) | $greatereq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))) <=> ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))) | (~sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))))) | $greatereq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(385,plain,
% 0.22/0.51 ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | ((~mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))) | (~sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))))) | $greatereq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(386,plain,
% 0.22/0.51 ((~![X: $int, Y: $int, L: list_int] : ((~mem(int, t2tb1(X), cons(int, t2tb1(Y), t2tb(L)))) | (~sorted1(tb2t(cons(int, t2tb1(Y), t2tb(L))))) | $greatereq($sum(X, $product(-1, Y)), 0))) | (~mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))) | (~sorted1(tb2t(cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11))))) | $greatereq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.22/0.51 tff(387,plain,
% 0.22/0.51 ((~mem(int, t2tb1(X!10), cons(int, t2tb1(tb2t1(t2tb1(X1!12))), t2tb(X2!11)))) | $greatereq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[386, 259, 383])).
% 0.22/0.51 tff(388,plain,
% 0.22/0.51 ($greatereq($sum(X!10, $product(-1, tb2t1(t2tb1(X1!12)))), 0)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[387, 377])).
% 0.22/0.51 tff(389,plain,
% 0.22/0.51 ($false),
% 0.22/0.51 inference(theory_lemma,[status(thm)],[388, 370, 17])).
% 0.22/0.51 tff(390,plain,((~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.51 tff(391,plain,
% 0.22/0.51 (((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | ((L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) & ((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | ((~($sum(X!10, $product(-1, X1!12)) = 0)) & (((~$lesseq($sum(X!10, $product(-1, X1!12)), 0)) & ((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))) | (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))))))))) <=> ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))))))))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(392,plain,
% 0.22/0.51 ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | ((L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11)))) & ((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | ((~($sum(X!10, $product(-1, X1!12)) = 0)) & (((~$lesseq($sum(X!10, $product(-1, X1!12)), 0)) & ((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9))))))) | (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0))))))))),
% 0.22/0.52 inference(and_elim,[status(thm)],[156])).
% 0.22/0.52 tff(393,plain,
% 0.22/0.52 ((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X1!12), t2tb(X2!11))))) | (~((~((~($sum(X!10, $product(-1, X1!12)) = 0)) | mem(int, t2tb1(X!10), t2tb(L!9)))) | (~(($sum(X!10, $product(-1, X1!12)) = 0) | (~((~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~$lesseq($sum(X!10, $product(-1, X1!12)), 0)))) | (~($lesseq($sum(X!10, $product(-1, X1!12)), 0) | (~((L!9 = tb2t(nil(int))) | (~((~(L!9 = tb2t(cons(int, t2tb1(X3!14), t2tb(X4!13))))) | (X4!13 = X2!11))) | (~sorted1(X2!11)) | (~(((~(Result!15 = true1)) <=> mem(int, t2tb1(X!10), t2tb(X2!11))) | ((Result!15 = true1) <=> mem(int, t2tb1(X!10), t2tb(L!9)))))))))))))))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.22/0.52 tff(394,plain,
% 0.22/0.52 (~((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int)))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[393, 390])).
% 0.22/0.52 tff(395,plain,
% 0.22/0.52 (((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int))))) | (L!9 = tb2t(nil(int)))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(396,plain,
% 0.22/0.52 (L!9 = tb2t(nil(int))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[395, 394])).
% 0.22/0.52 tff(397,plain,
% 0.22/0.52 (t2tb(L!9) = t2tb(tb2t(nil(int)))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[396])).
% 0.22/0.52 tff(398,plain,
% 0.22/0.52 (t2tb(tb2t(nil(int))) = t2tb(L!9)),
% 0.22/0.52 inference(symmetry,[status(thm)],[397])).
% 0.22/0.52 tff(399,plain,
% 0.22/0.52 (nil(int) = t2tb(L!9)),
% 0.22/0.52 inference(transitivity,[status(thm)],[94, 398])).
% 0.22/0.52 tff(400,plain,
% 0.22/0.52 (mem(int, t2tb1(X!10), nil(int)) <=> mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[399])).
% 0.22/0.52 tff(401,plain,
% 0.22/0.52 (mem(int, t2tb1(X!10), t2tb(L!9)) <=> mem(int, t2tb1(X!10), nil(int))),
% 0.22/0.52 inference(symmetry,[status(thm)],[400])).
% 0.22/0.52 tff(402,plain,
% 0.22/0.52 (((~mem(int, t2tb1(X!10), t2tb(L!9))) | (~(L!9 = tb2t(nil(int))))) | mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(403,plain,
% 0.22/0.52 (mem(int, t2tb1(X!10), t2tb(L!9))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[402, 394])).
% 0.22/0.52 tff(404,plain,
% 0.22/0.52 (mem(int, t2tb1(X!10), nil(int))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[403, 401])).
% 0.22/0.52 tff(405,plain,
% 0.22/0.52 ((~sort1(int, t2tb1(X!10))) | (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2)))))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[281, 208])).
% 0.22/0.52 tff(406,plain,
% 0.22/0.52 (~(mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2))))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[405, 190])).
% 0.22/0.52 tff(407,plain,
% 0.22/0.52 ((mem(int, t2tb1(X!10), nil(int)) | (~![X1: uni, X2: uni] : ((~sort1(int, X1)) | (mem(int, t2tb1(X!10), cons(int, X1, X2)) <=> ((t2tb1(X!10) = X1) | mem(int, t2tb1(X!10), X2)))))) | (~mem(int, t2tb1(X!10), nil(int)))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(408,plain,
% 0.22/0.52 (~mem(int, t2tb1(X!10), nil(int))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[407, 406])).
% 0.22/0.52 tff(409,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[408, 404])).
% 0.22/0.52 % SZS output end Proof
%------------------------------------------------------------------------------