TSTP Solution File: SWC404+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC404+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Tue Sep 20 11:57:44 EDT 2022
% Result : Theorem 16.14s 10.56s
% Output : Proof 16.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWC404+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n002.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun Sep 4 00:57:02 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 16.14/10.56 % SZS status Theorem
% 16.14/10.56 % SZS output start Proof
% 16.14/10.56 tff(memberP_type, type, (
% 16.14/10.56 memberP: ( $i * $i ) > $o)).
% 16.14/10.56 tff(tptp_fun_X9_53_type, type, (
% 16.14/10.56 tptp_fun_X9_53: $i)).
% 16.14/10.56 tff(app_type, type, (
% 16.14/10.56 app: ( $i * $i ) > $i)).
% 16.14/10.56 tff(tptp_fun_Z_52_type, type, (
% 16.14/10.56 tptp_fun_Z_52: $i)).
% 16.14/10.56 tff(tptp_fun_W_49_type, type, (
% 16.14/10.56 tptp_fun_W_49: $i)).
% 16.14/10.56 tff(tptp_fun_Y_51_type, type, (
% 16.14/10.56 tptp_fun_Y_51: $i)).
% 16.14/10.56 tff(tptp_fun_V_48_type, type, (
% 16.14/10.56 tptp_fun_V_48: $i)).
% 16.14/10.56 tff(tptp_fun_X_50_type, type, (
% 16.14/10.56 tptp_fun_X_50: $i)).
% 16.14/10.56 tff(tptp_fun_U_47_type, type, (
% 16.14/10.56 tptp_fun_U_47: $i)).
% 16.14/10.56 tff(ssItem_type, type, (
% 16.14/10.56 ssItem: $i > $o)).
% 16.14/10.56 tff(lt_type, type, (
% 16.14/10.56 lt: ( $i * $i ) > $o)).
% 16.14/10.56 tff(cons_type, type, (
% 16.14/10.56 cons: ( $i * $i ) > $i)).
% 16.14/10.56 tff(nil_type, type, (
% 16.14/10.56 nil: $i)).
% 16.14/10.56 tff(ssList_type, type, (
% 16.14/10.56 ssList: $i > $o)).
% 16.14/10.56 tff(strictorderedP_type, type, (
% 16.14/10.56 strictorderedP: $i > $o)).
% 16.14/10.56 tff(1,plain,
% 16.14/10.56 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(2,plain,
% 16.14/10.56 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(3,plain,
% 16.14/10.56 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(4,plain,
% 16.14/10.56 (((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(5,plain,
% 16.14/10.56 ((~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))) <=> (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(6,plain,
% 16.14/10.56 ((ssList(Y!51) & (strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) <=> (ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(7,plain,
% 16.14/10.56 (((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5))))))) <=> (strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(8,plain,
% 16.14/10.56 ((~(~ssList(Y!51))) <=> ssList(Y!51)),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(9,plain,
% 16.14/10.56 (((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) <=> (ssList(Y!51) & (strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5))))))))),
% 16.14/10.56 inference(monotonicity,[status(thm)],[8, 7])).
% 16.14/10.56 tff(10,plain,
% 16.14/10.56 (((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) <=> (ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))),
% 16.14/10.56 inference(transitivity,[status(thm)],[9, 6])).
% 16.14/10.56 tff(11,plain,
% 16.14/10.56 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(12,plain,
% 16.14/10.56 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(13,plain,
% 16.14/10.56 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 16.14/10.56 inference(rewrite,[status(thm)],[])).
% 16.14/10.56 tff(14,plain,
% 16.14/10.56 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.57 inference(monotonicity,[status(thm)],[13, 12, 11, 10, 5])).
% 16.14/10.57 tff(15,plain,
% 16.14/10.57 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.57 inference(transitivity,[status(thm)],[14, 4])).
% 16.14/10.57 tff(16,plain,
% 16.14/10.57 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(17,plain,
% 16.14/10.57 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))))),
% 16.14/10.57 inference(monotonicity,[status(thm)],[16, 15])).
% 16.14/10.57 tff(18,plain,
% 16.14/10.57 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.57 inference(transitivity,[status(thm)],[17, 3])).
% 16.14/10.57 tff(19,plain,
% 16.14/10.57 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(20,plain,
% 16.14/10.57 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))))),
% 16.14/10.57 inference(monotonicity,[status(thm)],[19, 18])).
% 16.14/10.57 tff(21,plain,
% 16.14/10.57 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.57 inference(transitivity,[status(thm)],[20, 2])).
% 16.14/10.57 tff(22,plain,
% 16.14/10.57 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(23,plain,
% 16.14/10.57 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))))),
% 16.14/10.57 inference(monotonicity,[status(thm)],[22, 21])).
% 16.14/10.57 tff(24,plain,
% 16.14/10.57 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~strictorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))))),
% 16.14/10.57 inference(transitivity,[status(thm)],[23, 1])).
% 16.14/10.57 tff(25,plain,
% 16.14/10.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9))))))))),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(26,plain,
% 16.14/10.57 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~strictorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = W)) & lt(X1, X3)))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(cons(X5, nil), X6) = Z)) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : ((ssList(X8) & (app(X8, cons(X7, nil)) = W)) & lt(X7, X5))))))))) | ![X9: $i] : (ssItem(X9) => ((~memberP(U, X9)) | memberP(V, X9)))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9))))))))),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(27,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~strictorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = W)) & lt(X1, X3)))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(cons(X5, nil), X6) = Z)) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : ((ssList(X8) & (app(X8, cons(X7, nil)) = W)) & lt(X7, X5))))))))) | ![X9: $i] : (ssItem(X9) => ((~memberP(U, X9)) | memberP(V, X9)))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 16.14/10.57 tff(28,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[27, 26])).
% 16.14/10.57 tff(29,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[28, 25])).
% 16.14/10.57 tff(30,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[29, 25])).
% 16.14/10.57 tff(31,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[30, 25])).
% 16.14/10.57 tff(32,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[31, 25])).
% 16.14/10.57 tff(33,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[32, 25])).
% 16.14/10.57 tff(34,plain,
% 16.14/10.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & lt(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & lt(X7, X5))))))) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[33, 25])).
% 16.14/10.57 tff(35,plain,
% 16.14/10.57 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & strictorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & lt(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & lt(X7, X5)))))) & (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[34, 24])).
% 16.14/10.57 tff(36,plain,
% 16.14/10.57 (V!48 = X!50),
% 16.14/10.57 inference(and_elim,[status(thm)],[35])).
% 16.14/10.57 tff(37,plain,
% 16.14/10.57 (X!50 = V!48),
% 16.14/10.57 inference(symmetry,[status(thm)],[36])).
% 16.14/10.57 tff(38,plain,
% 16.14/10.57 (app(app(Y!51, W!49), Z!52) = X!50),
% 16.14/10.57 inference(and_elim,[status(thm)],[35])).
% 16.14/10.57 tff(39,plain,
% 16.14/10.57 (app(app(Y!51, W!49), Z!52) = V!48),
% 16.14/10.57 inference(transitivity,[status(thm)],[38, 37])).
% 16.14/10.57 tff(40,plain,
% 16.14/10.57 (memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> memberP(V!48, X9!53)),
% 16.14/10.57 inference(monotonicity,[status(thm)],[39])).
% 16.14/10.57 tff(41,plain,
% 16.14/10.57 (memberP(V!48, X9!53) <=> memberP(app(app(Y!51, W!49), Z!52), X9!53)),
% 16.14/10.57 inference(symmetry,[status(thm)],[40])).
% 16.14/10.57 tff(42,plain,
% 16.14/10.57 ((~memberP(V!48, X9!53)) <=> (~memberP(app(app(Y!51, W!49), Z!52), X9!53))),
% 16.14/10.57 inference(monotonicity,[status(thm)],[41])).
% 16.14/10.57 tff(43,plain,
% 16.14/10.57 (~(memberP(V!48, X9!53) | (~ssItem(X9!53)) | (~memberP(U!47, X9!53)))),
% 16.14/10.57 inference(and_elim,[status(thm)],[35])).
% 16.14/10.57 tff(44,plain,
% 16.14/10.57 (~memberP(V!48, X9!53)),
% 16.14/10.57 inference(or_elim,[status(thm)],[43])).
% 16.14/10.57 tff(45,plain,
% 16.14/10.57 (~memberP(app(app(Y!51, W!49), Z!52), X9!53)),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[44, 42])).
% 16.14/10.57 tff(46,plain,
% 16.14/10.57 (ssList(Y!51)),
% 16.14/10.57 inference(and_elim,[status(thm)],[35])).
% 16.14/10.57 tff(47,plain,
% 16.14/10.57 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 16.14/10.57 inference(bind,[status(th)],[])).
% 16.14/10.57 tff(48,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(quant_intro,[status(thm)],[47])).
% 16.14/10.57 tff(49,plain,
% 16.14/10.57 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 16.14/10.57 inference(bind,[status(th)],[])).
% 16.14/10.57 tff(50,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(quant_intro,[status(thm)],[49])).
% 16.14/10.57 tff(51,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(transitivity,[status(thm)],[50, 48])).
% 16.14/10.57 tff(52,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(53,plain,
% 16.14/10.57 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ssList(app(U, V))) <=> ((~ssList(V)) | ssList(app(U, V))))), (![V: $i] : (ssList(V) => ssList(app(U, V))) <=> ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))))),
% 16.14/10.57 inference(bind,[status(th)],[])).
% 16.14/10.57 tff(54,plain,
% 16.14/10.57 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(quant_intro,[status(thm)],[53])).
% 16.14/10.57 tff(55,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax26')).
% 16.14/10.57 tff(56,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[55, 54])).
% 16.14/10.57 tff(57,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[56, 52])).
% 16.14/10.57 tff(58,plain,(
% 16.14/10.57 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(skolemize,[status(sab)],[57])).
% 16.14/10.57 tff(59,plain,
% 16.14/10.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[58, 51])).
% 16.14/10.57 tff(60,plain,
% 16.14/10.57 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V))))),
% 16.14/10.57 inference(rewrite,[status(thm)],[])).
% 16.14/10.57 tff(61,plain,
% 16.14/10.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V))))),
% 16.14/10.57 inference(quant_inst,[status(thm)],[])).
% 16.14/10.57 tff(62,plain,
% 16.14/10.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))),
% 16.14/10.57 inference(modus_ponens,[status(thm)],[61, 60])).
% 16.14/10.57 tff(63,plain,
% 16.14/10.57 (![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))),
% 16.14/10.57 inference(unit_resolution,[status(thm)],[62, 59, 46])).
% 16.14/10.57 tff(64,plain,
% 16.14/10.57 (ssList(W!49)),
% 16.14/10.57 inference(and_elim,[status(thm)],[35])).
% 16.14/10.58 tff(65,plain,
% 16.14/10.58 (((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | ((~ssList(W!49)) | ssList(app(Y!51, W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | (~ssList(W!49)) | ssList(app(Y!51, W!49)))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(66,plain,
% 16.14/10.58 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | ((~ssList(W!49)) | ssList(app(Y!51, W!49)))),
% 16.14/10.58 inference(quant_inst,[status(thm)],[])).
% 16.14/10.58 tff(67,plain,
% 16.14/10.58 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | (~ssList(W!49)) | ssList(app(Y!51, W!49))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[66, 65])).
% 16.14/10.58 tff(68,plain,
% 16.14/10.58 (ssList(app(Y!51, W!49))),
% 16.14/10.58 inference(unit_resolution,[status(thm)],[67, 64, 63])).
% 16.14/10.58 tff(69,plain,
% 16.14/10.58 (ssItem(X9!53)),
% 16.14/10.58 inference(or_elim,[status(thm)],[43])).
% 16.14/10.58 tff(70,plain,
% 16.14/10.58 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 16.14/10.58 inference(bind,[status(th)],[])).
% 16.14/10.58 tff(71,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(quant_intro,[status(thm)],[70])).
% 16.14/10.58 tff(72,plain,
% 16.14/10.58 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 16.14/10.58 inference(bind,[status(th)],[])).
% 16.14/10.58 tff(73,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(quant_intro,[status(thm)],[72])).
% 16.14/10.58 tff(74,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(transitivity,[status(thm)],[73, 71])).
% 16.14/10.58 tff(75,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(76,plain,
% 16.14/10.58 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))) <=> (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> (ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), rewrite((ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), (![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))))),
% 16.14/10.58 inference(bind,[status(th)],[])).
% 16.14/10.58 tff(77,plain,
% 16.14/10.58 (![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(quant_intro,[status(thm)],[76])).
% 16.14/10.58 tff(78,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax36')).
% 16.14/10.58 tff(79,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[78, 77])).
% 16.14/10.58 tff(80,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[79, 75])).
% 16.14/10.58 tff(81,plain,(
% 16.14/10.58 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(skolemize,[status(sab)],[80])).
% 16.14/10.58 tff(82,plain,
% 16.14/10.58 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[81, 74])).
% 16.14/10.58 tff(83,plain,
% 16.14/10.58 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X9!53)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X9!53)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53))))))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(84,plain,
% 16.14/10.58 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X9!53)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53))))))),
% 16.14/10.58 inference(quant_inst,[status(thm)],[])).
% 16.14/10.58 tff(85,plain,
% 16.14/10.58 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X9!53)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[84, 83])).
% 16.14/10.58 tff(86,plain,
% 16.14/10.58 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))),
% 16.14/10.58 inference(unit_resolution,[status(thm)],[85, 82, 69])).
% 16.14/10.58 tff(87,plain,
% 16.14/10.58 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | ((~ssList(app(Y!51, W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | (~ssList(app(Y!51, W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53)))))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(88,plain,
% 16.14/10.58 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | ((~ssList(app(Y!51, W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53)))))),
% 16.14/10.58 inference(quant_inst,[status(thm)],[])).
% 16.14/10.58 tff(89,plain,
% 16.14/10.58 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | (~ssList(app(Y!51, W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53))))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[88, 87])).
% 16.14/10.58 tff(90,plain,
% 16.14/10.58 (![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53))))),
% 16.14/10.58 inference(unit_resolution,[status(thm)],[89, 86, 68])).
% 16.14/10.58 tff(91,plain,
% 16.14/10.58 (ssList(Z!52)),
% 16.14/10.58 inference(and_elim,[status(thm)],[35])).
% 16.14/10.58 tff(92,plain,
% 16.14/10.58 (((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53))))) | ((~ssList(Z!52)) | (memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53))))) | (~ssList(Z!52)) | (memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53))))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(93,plain,
% 16.14/10.58 ((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53))))) | ((~ssList(Z!52)) | (memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53))))),
% 16.14/10.58 inference(quant_inst,[status(thm)],[])).
% 16.14/10.58 tff(94,plain,
% 16.14/10.58 ((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!51, W!49), W), X9!53) <=> (memberP(W, X9!53) | memberP(app(Y!51, W!49), X9!53))))) | (~ssList(Z!52)) | (memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53)))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[93, 92])).
% 16.14/10.58 tff(95,plain,
% 16.14/10.58 (memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53))),
% 16.14/10.58 inference(unit_resolution,[status(thm)],[94, 91, 90])).
% 16.14/10.58 tff(96,plain,
% 16.14/10.58 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | ((~ssList(Y!51)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | (~ssList(Y!51)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53)))))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(97,plain,
% 16.14/10.58 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | ((~ssList(Y!51)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53)))))),
% 16.14/10.58 inference(quant_inst,[status(thm)],[])).
% 16.14/10.58 tff(98,plain,
% 16.14/10.58 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!53) <=> (memberP(W, X9!53) | memberP(V, X9!53)))))) | (~ssList(Y!51)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53))))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[97, 96])).
% 16.14/10.58 tff(99,plain,
% 16.14/10.58 (![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53))))),
% 16.14/10.58 inference(unit_resolution,[status(thm)],[98, 46, 86])).
% 16.14/10.58 tff(100,plain,
% 16.14/10.58 (((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53))))) | ((~ssList(W!49)) | (memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53))))) | (~ssList(W!49)) | (memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53))))),
% 16.14/10.58 inference(rewrite,[status(thm)],[])).
% 16.14/10.58 tff(101,plain,
% 16.14/10.58 ((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53))))) | ((~ssList(W!49)) | (memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53))))),
% 16.14/10.58 inference(quant_inst,[status(thm)],[])).
% 16.14/10.58 tff(102,plain,
% 16.14/10.58 ((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!51, W), X9!53) <=> (memberP(W, X9!53) | memberP(Y!51, X9!53))))) | (~ssList(W!49)) | (memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53)))),
% 16.14/10.58 inference(modus_ponens,[status(thm)],[101, 100])).
% 16.14/10.58 tff(103,plain,
% 16.14/10.58 (memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53))),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[102, 64, 99])).
% 16.14/10.60 tff(104,plain,
% 16.14/10.60 (U!47 = W!49),
% 16.14/10.60 inference(and_elim,[status(thm)],[35])).
% 16.14/10.60 tff(105,plain,
% 16.14/10.60 (W!49 = U!47),
% 16.14/10.60 inference(symmetry,[status(thm)],[104])).
% 16.14/10.60 tff(106,plain,
% 16.14/10.60 (memberP(W!49, X9!53) <=> memberP(U!47, X9!53)),
% 16.14/10.60 inference(monotonicity,[status(thm)],[105])).
% 16.14/10.60 tff(107,plain,
% 16.14/10.60 (memberP(U!47, X9!53) <=> memberP(W!49, X9!53)),
% 16.14/10.60 inference(symmetry,[status(thm)],[106])).
% 16.14/10.60 tff(108,plain,
% 16.14/10.60 (memberP(U!47, X9!53)),
% 16.14/10.60 inference(or_elim,[status(thm)],[43])).
% 16.14/10.60 tff(109,plain,
% 16.14/10.60 (memberP(W!49, X9!53)),
% 16.14/10.60 inference(modus_ponens,[status(thm)],[108, 107])).
% 16.14/10.60 tff(110,plain,
% 16.14/10.60 ((memberP(W!49, X9!53) | memberP(Y!51, X9!53)) | (~memberP(W!49, X9!53))),
% 16.14/10.60 inference(tautology,[status(thm)],[])).
% 16.14/10.60 tff(111,plain,
% 16.14/10.60 (memberP(W!49, X9!53) | memberP(Y!51, X9!53)),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[110, 109])).
% 16.14/10.60 tff(112,plain,
% 16.14/10.60 ((~(memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53)))) | memberP(app(Y!51, W!49), X9!53) | (~(memberP(W!49, X9!53) | memberP(Y!51, X9!53)))),
% 16.14/10.60 inference(tautology,[status(thm)],[])).
% 16.14/10.60 tff(113,plain,
% 16.14/10.60 ((~(memberP(app(Y!51, W!49), X9!53) <=> (memberP(W!49, X9!53) | memberP(Y!51, X9!53)))) | memberP(app(Y!51, W!49), X9!53)),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[112, 111])).
% 16.14/10.60 tff(114,plain,
% 16.14/10.60 (memberP(app(Y!51, W!49), X9!53)),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[113, 103])).
% 16.14/10.60 tff(115,plain,
% 16.14/10.60 ((memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53)) | (~memberP(app(Y!51, W!49), X9!53))),
% 16.14/10.60 inference(tautology,[status(thm)],[])).
% 16.14/10.60 tff(116,plain,
% 16.14/10.60 (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53)),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[115, 114])).
% 16.14/10.60 tff(117,plain,
% 16.14/10.60 ((~(memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53)))) | memberP(app(app(Y!51, W!49), Z!52), X9!53) | (~(memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53)))),
% 16.14/10.60 inference(tautology,[status(thm)],[])).
% 16.14/10.60 tff(118,plain,
% 16.14/10.60 ((~(memberP(app(app(Y!51, W!49), Z!52), X9!53) <=> (memberP(Z!52, X9!53) | memberP(app(Y!51, W!49), X9!53)))) | memberP(app(app(Y!51, W!49), Z!52), X9!53)),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[117, 116])).
% 16.14/10.60 tff(119,plain,
% 16.14/10.60 (memberP(app(app(Y!51, W!49), Z!52), X9!53)),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[118, 95])).
% 16.14/10.60 tff(120,plain,
% 16.14/10.60 ($false),
% 16.14/10.60 inference(unit_resolution,[status(thm)],[119, 45])).
% 16.14/10.60 % SZS output end Proof
%------------------------------------------------------------------------------