TSTP Solution File: SWW624_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW624_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:29 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW624_2 : TPTP v8.1.0. Released v6.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 20:34:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(num_occ_type, type, (
% 0.20/0.45 num_occ: ( ty * uni * uni ) > $int)).
% 0.20/0.45 tff(prefix_type, type, (
% 0.20/0.45 prefix: ( ty * $int * uni ) > uni)).
% 0.20/0.45 tff(nil_type, type, (
% 0.20/0.45 nil: ty > uni)).
% 0.20/0.45 tff(elt1_type, type, (
% 0.20/0.45 elt1: ty)).
% 0.20/0.45 tff(length_type, type, (
% 0.20/0.45 length: ( ty * uni ) > $int)).
% 0.20/0.45 tff(tptp_fun_X_2_type, type, (
% 0.20/0.45 tptp_fun_X_2: ( uni * uni * ty ) > uni)).
% 0.20/0.45 tff(sort_type, type, (
% 0.20/0.45 sort: ( ty * uni ) > $o)).
% 0.20/0.45 tff(permut_type, type, (
% 0.20/0.45 permut: ( ty * uni * uni ) > $o)).
% 0.20/0.45 tff(cons_type, type, (
% 0.20/0.45 cons: ( ty * uni * uni ) > uni)).
% 0.20/0.45 tff(t2tb_type, type, (
% 0.20/0.45 t2tb: list_elt > uni)).
% 0.20/0.45 tff(tptp_fun_X1_11_type, type, (
% 0.20/0.45 tptp_fun_X1_11: list_elt)).
% 0.20/0.45 tff(t2tb1_type, type, (
% 0.20/0.45 t2tb1: elt > uni)).
% 0.20/0.45 tff(tptp_fun_X_12_type, type, (
% 0.20/0.45 tptp_fun_X_12: elt)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[A: ty, L1: uni, L2: uni] : refl((~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))) <=> (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))) <=> ![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (^[A: ty, L1: uni, L2: uni] : rewrite((~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))) <=> (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))) <=> ![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))) <=> ![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (^[A: ty, L1: uni, L2: uni] : trans(monotonicity(rewrite(((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) <=> ((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))), ((((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))) <=> (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))))), rewrite((((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))) <=> (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))), ((((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))) <=> (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (^[A: ty, L1: uni, L2: uni] : rewrite((((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0))) | permut(A, L1, L2))) <=> (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | permut(A, L1, L2))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0))) | permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | permut(A, L1, L2)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (^[A: ty, L1: uni, L2: uni] : rewrite((((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2))) <=> (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0))) | permut(A, L1, L2))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (^[A: ty, L1: uni, L2: uni] : rewrite(((permut(A, L1, L2) => ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & (![X: uni] : (sort(A, X) => (num_occ(A, X, L1) = num_occ(A, X, L2))) => permut(A, L1, L2))) <=> (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : ((permut(A, L1, L2) => ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & (![X: uni] : (sort(A, X) => (num_occ(A, X, L1) = num_occ(A, X, L2))) => permut(A, L1, L2))) <=> ![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.46 tff(15,axiom,(![A: ty, L1: uni, L2: uni] : ((permut(A, L1, L2) => ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & (![X: uni] : (sort(A, X) => (num_occ(A, X, L1) = num_occ(A, X, L2))) => permut(A, L1, L2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_def')).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : (num_occ(A, X, L1) = num_occ(A, X, L2))) & ((~![X: uni] : ((~sort(A, X)) | (num_occ(A, X, L1) = num_occ(A, X, L2)))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L1), $product(-1, num_occ(A, X, L2))) = 0))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~![X: uni] : ((~sort(A, X)) | ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[18, 9])).
% 0.20/0.46 tff(20,plain,(
% 0.20/0.46 ![A: ty, L1: uni, L2: uni] : (((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0)) & ((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[19])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 (![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.20/0.46 tff(23,plain,
% 0.20/0.46 ((~![A: ty, L1: uni, L2: uni] : (~((~((~permut(A, L1, L2)) | ![X: uni] : ($sum(num_occ(A, X, L2), $product(-1, num_occ(A, X, L1))) = 0))) | (~((~((~sort(A, tptp_fun_X_2(L2, L1, A))) | ($sum(num_occ(A, tptp_fun_X_2(L2, L1, A), L2), $product(-1, num_occ(A, tptp_fun_X_2(L2, L1, A), L1))) = 0))) | permut(A, L1, L2)))))) | (~((~((~permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1))) | ![X: uni] : ($sum(num_occ(elt1, X, nil(elt1)), $product(-1, num_occ(elt1, X, prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | (~((~((~sort(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1))) | ($sum(num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), nil(elt1)), $product(-1, num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (~((~((~permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1))) | ![X: uni] : ($sum(num_occ(elt1, X, nil(elt1)), $product(-1, num_occ(elt1, X, prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | (~((~((~sort(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1))) | ($sum(num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), nil(elt1)), $product(-1, num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (((~((~permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1))) | ![X: uni] : ($sum(num_occ(elt1, X, nil(elt1)), $product(-1, num_occ(elt1, X, prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | (~((~((~sort(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1))) | ($sum(num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), nil(elt1)), $product(-1, num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1))))) | ((~((~sort(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1))) | ($sum(num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), nil(elt1)), $product(-1, num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 ((~((~sort(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1))) | ($sum(num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), nil(elt1)), $product(-1, num_occ(elt1, tptp_fun_X_2(nil(elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), elt1), prefix(elt1, length(elt1, nil(elt1)), nil(elt1))))) = 0))) | permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (^[A: ty, L: uni] : refl($greatereq(length(A, L), 0) <=> $greatereq(length(A, L), 0))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (![A: ty, L: uni] : $greatereq(length(A, L), 0) <=> ![A: ty, L: uni] : $greatereq(length(A, L), 0)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (^[A: ty, L: uni] : rewrite($lesseq(0, length(A, L)) <=> $greatereq(length(A, L), 0))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (![A: ty, L: uni] : $lesseq(0, length(A, L)) <=> ![A: ty, L: uni] : $greatereq(length(A, L), 0)),
% 0.20/0.46 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (![A: ty, L: uni] : $lesseq(0, length(A, L)) <=> ![A: ty, L: uni] : $lesseq(0, length(A, L))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(32,axiom,(![A: ty, L: uni] : $lesseq(0, length(A, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_nonnegative')).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (![A: ty, L: uni] : $lesseq(0, length(A, L))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (![A: ty, L: uni] : $greatereq(length(A, L), 0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.20/0.46 tff(35,plain,(
% 0.20/0.46 ![A: ty, L: uni] : $greatereq(length(A, L), 0)),
% 0.20/0.46 inference(skolemize,[status(sab)],[34])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (![A: ty, L: uni] : $greatereq(length(A, L), 0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 ((~![A: ty, L: uni] : $greatereq(length(A, L), 0)) | $greatereq(length(elt1, t2tb(X1!11)), 0)),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 ($greatereq(length(elt1, t2tb(X1!11)), 0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (^[A: ty] : refl((~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))) <=> (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))) <=> ![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (^[A: ty] : rewrite((~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))) <=> (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 (![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))) <=> ![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))) <=> ![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (^[A: ty] : rewrite(((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)) <=> (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)) <=> ![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (^[A: ty] : rewrite(((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, cons(A, X, X1)), $product(-1, length(A, X1))) = 1)) <=> ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, cons(A, X, X1)), $product(-1, length(A, X1))) = 1)) <=> ![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (^[A: ty] : rewrite(((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length(A, cons(A, X, X1)) = $sum(1, length(A, X1)))) <=> ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, cons(A, X, X1)), $product(-1, length(A, X1))) = 1)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length(A, cons(A, X, X1)) = $sum(1, length(A, X1)))) <=> ![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, cons(A, X, X1)), $product(-1, length(A, X1))) = 1))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length(A, cons(A, X, X1)) = $sum(1, length(A, X1)))) <=> ![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length(A, cons(A, X, X1)) = $sum(1, length(A, X1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(51,axiom,(![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length(A, cons(A, X, X1)) = $sum(1, length(A, X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_def')).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : (length(A, cons(A, X, X1)) = $sum(1, length(A, X1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, cons(A, X, X1)), $product(-1, length(A, X1))) = 1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[53, 47])).
% 0.20/0.46 tff(55,plain,(
% 0.20/0.46 ![A: ty] : ((length(A, nil(A)) = 0) & ![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))),
% 0.20/0.46 inference(skolemize,[status(sab)],[54])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 (![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[56, 43])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 ((~![A: ty] : (~((~(length(A, nil(A)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(A, X1), $product(-1, length(A, cons(A, X, X1)))) = -1))))) | (~((~(length(elt1, nil(elt1)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(elt1, X1), $product(-1, length(elt1, cons(elt1, X, X1)))) = -1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (~((~(length(elt1, nil(elt1)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(elt1, X1), $product(-1, length(elt1, cons(elt1, X, X1)))) = -1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (((~(length(elt1, nil(elt1)) = 0)) | (~![X: uni, X1: uni] : ($sum(length(elt1, X1), $product(-1, length(elt1, cons(elt1, X, X1)))) = -1))) | ![X: uni, X1: uni] : ($sum(length(elt1, X1), $product(-1, length(elt1, cons(elt1, X, X1)))) = -1)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.47 (![X: uni, X1: uni] : ($sum(length(elt1, X1), $product(-1, length(elt1, cons(elt1, X, X1)))) = -1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 ((~![X: uni, X1: uni] : ($sum(length(elt1, X1), $product(-1, length(elt1, cons(elt1, X, X1)))) = -1)) | ($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))) = -1)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))) = -1),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ((~($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))) = -1)) | $lesseq($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))), -1)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 ($lesseq($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))), -1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 ((~$lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0)) | (~$greatereq(length(elt1, t2tb(X1!11)), 0)) | (~$lesseq($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))), -1))),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (~$lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[66, 65, 38])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (^[A: ty, N: $int, X: uni, L: uni] : refl(($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))) <=> ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))) <=> ![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))) <=> ![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (^[A: ty, N: $int, X: uni, L: uni] : trans(monotonicity(rewrite($less(0, N) <=> (~$lesseq(N, 0))), rewrite((prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $difference(N, 1), L))) <=> (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))), (($less(0, N) => (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $difference(N, 1), L)))) <=> ((~$lesseq(N, 0)) => (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))))), rewrite(((~$lesseq(N, 0)) => (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L)))) <=> ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))), (($less(0, N) => (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $difference(N, 1), L)))) <=> ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 (![A: ty, N: $int, X: uni, L: uni] : ($less(0, N) => (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $difference(N, 1), L)))) <=> ![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.47 tff(73,axiom,(![A: ty, N: $int, X: uni, L: uni] : ($less(0, N) => (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $difference(N, 1), L))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prefix_def2')).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.47 tff(76,plain,(
% 0.20/0.47 ![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[75])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 (![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (((~![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))) | ($lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0) | (prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11)))))) <=> ((~![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))) | $lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0) | (prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 ((~![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))) | ($lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0) | (prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 ((~![A: ty, N: $int, X: uni, L: uni] : ($lesseq(N, 0) | (prefix(A, N, cons(A, X, L)) = cons(A, X, prefix(A, $sum(-1, N), L))))) | $lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0) | (prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 ($lesseq(length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), 0) | (prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[81, 67])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11))) = prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[82])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 ((~($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))) = -1)) | $greatereq($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))), -1)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 ($greatereq($sum(length(elt1, t2tb(X1!11)), $product(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))), -1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[84, 63])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (length(elt1, t2tb(X1!11)) = $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))))),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[85, 65])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 ($sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))) = length(elt1, t2tb(X1!11))),
% 0.20/0.47 inference(symmetry,[status(thm)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11)) = prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[87])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)) = prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11))),
% 0.20/0.47 inference(symmetry,[status(thm)],[88])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))) = cons(elt1, t2tb1(X!12), prefix(elt1, $sum(-1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11)))), t2tb(X1!11)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))) = prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[90, 83])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) <=> permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))) <=> permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[92])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 ((~permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))) <=> (~permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.47 tff(95,assumption,(~((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))))), introduced(assumption)).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))) | (~permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(97,plain,
% 0.20/0.47 (~permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (~permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))) | permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 (permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (^[A: ty, X: uni, L1: uni, L2: uni] : refl(((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2))) <=> ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (^[A: ty, X: uni, L1: uni, L2: uni] : rewrite((permut(A, L1, L2) => permut(A, cons(A, X, L1), cons(A, X, L2))) <=> ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (![A: ty, X: uni, L1: uni, L2: uni] : (permut(A, L1, L2) => permut(A, cons(A, X, L1), cons(A, X, L2))) <=> ![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.47 tff(106,axiom,(![A: ty, X: uni, L1: uni, L2: uni] : (permut(A, L1, L2) => permut(A, cons(A, X, L1), cons(A, X, L2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_cons')).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.47 tff(109,plain,(
% 0.20/0.47 ![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[108])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (((~![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))) | ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))))) <=> ((~![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))) | (~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((~![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))) | ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 ((~![A: ty, X: uni, L1: uni, L2: uni] : ((~permut(A, L1, L2)) | permut(A, cons(A, X, L1), cons(A, X, L2)))) | (~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (permut(elt1, cons(elt1, t2tb1(X!12), prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[114, 98])).
% 0.20/0.47 tff(116,plain,((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1!11)), t2tb(X1!11)), t2tb(X1!11))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11))), cons(elt1, t2tb1(X!12), t2tb(X1!11)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 ((permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))))) <=> (permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 ((~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))) <=> (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 ((~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))) <=> (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : (permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1)) => permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))) <=> (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(121,axiom,(~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : (permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1)) => permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permut_prefix')).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 118])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[126, 118])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (~(permut(elt1, prefix(elt1, length(elt1, nil(elt1)), nil(elt1)), nil(elt1)) & ![X: elt, X1: list_elt] : ((~permut(elt1, prefix(elt1, length(elt1, t2tb(X1)), t2tb(X1)), t2tb(X1))) | permut(elt1, prefix(elt1, length(elt1, cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1))), cons(elt1, t2tb1(X), t2tb(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[127, 118])).
% 0.20/0.48 unexpected number of arguments: (let ((a!1 (permut elt1
% 0.20/0.48 (prefix elt1 (length elt1 (nil elt1)) (nil elt1))
% 0.20/0.48 (nil elt1)))
% 0.20/0.48 (a!2 (forall ((X elt) (X1 list_elt))
% 0.20/0.48 (let ((a!1 (permut elt1
% 0.20/0.48 (prefix elt1 (length elt1 (t2tb X1)) (t2tb X1))
% 0.20/0.48 (t2tb X1)))
% 0.20/0.48 (a!2 (prefix elt1
% 0.20/0.48 (length elt1 (cons elt1 (t2tb1 X) (t2tb X1)))
% 0.20/0.48 (cons elt1 (t2tb1 X) (t2tb X1)))))
% 0.20/0.48 (or (not a!1) (permut elt1 a!2 (cons elt1 (t2tb1 X) (t2tb X1)))))))
% 0.20/0.48 (a!3 (permut elt1
% 0.20/0.48 (prefix elt1 (length elt1 (t2tb X1!11)) (t2tb X1!11))
% 0.20/0.48 (t2tb X1!11)))
% 0.20/0.48 (a!4 (prefix elt1
% 0.20/0.48 (length elt1 (cons elt1 (t2tb1 X!12) (t2tb X1!11)))
% 0.20/0.48 (cons elt1 (t2tb1 X!12) (t2tb X1!11)))))
% 0.20/0.48 (let ((a!5 (or (not a!3)
% 0.20/0.48 (permut elt1 a!4 (cons elt1 (t2tb1 X!12) (t2tb X1!11))))))
% 0.20/0.48 (nnf-neg (refl (~ (not a!1) (not a!1)))
% 0.20/0.48 (sk (~ (not a!2) (not a!5)))
% 0.20/0.48 (~ (not (and a!1 a!2)) (or (not a!1) (not a!5))))))
% 0.20/0.48 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------