TSTP Solution File: SWC279+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC279+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 11:56:47 EDT 2022
% Result : Theorem 16.17s 10.65s
% Output : Proof 16.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC279+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n010.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 : Sat Sep 3 23:20:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 16.17/10.65 % SZS status Theorem
% 16.17/10.65 % SZS output start Proof
% 16.17/10.65 tff(leq_type, type, (
% 16.17/10.65 leq: ( $i * $i ) > $o)).
% 16.17/10.65 tff(tptp_fun_X3_51_type, type, (
% 16.17/10.65 tptp_fun_X3_51: $i)).
% 16.17/10.65 tff(tptp_fun_X6_54_type, type, (
% 16.17/10.65 tptp_fun_X6_54: $i)).
% 16.17/10.65 tff(memberP_type, type, (
% 16.17/10.65 memberP: ( $i * $i ) > $o)).
% 16.17/10.65 tff(tptp_fun_X4_52_type, type, (
% 16.17/10.65 tptp_fun_X4_52: $i)).
% 16.17/10.65 tff(tptp_fun_X5_53_type, type, (
% 16.17/10.65 tptp_fun_X5_53: $i)).
% 16.17/10.65 tff(ssItem_type, type, (
% 16.17/10.65 ssItem: $i > $o)).
% 16.17/10.65 tff(tptp_fun_W_49_type, type, (
% 16.17/10.65 tptp_fun_W_49: $i)).
% 16.17/10.65 tff(app_type, type, (
% 16.17/10.65 app: ( $i * $i ) > $i)).
% 16.17/10.65 tff(cons_type, type, (
% 16.17/10.65 cons: ( $i * $i ) > $i)).
% 16.17/10.65 tff(nil_type, type, (
% 16.17/10.65 nil: $i)).
% 16.17/10.65 tff(tptp_fun_U_47_type, type, (
% 16.17/10.65 tptp_fun_U_47: $i)).
% 16.17/10.65 tff(ssList_type, type, (
% 16.17/10.65 ssList: $i > $o)).
% 16.17/10.65 tff(tptp_fun_X_50_type, type, (
% 16.17/10.65 tptp_fun_X_50: $i)).
% 16.17/10.65 tff(tptp_fun_V_48_type, type, (
% 16.17/10.65 tptp_fun_V_48: $i)).
% 16.17/10.65 tff(1,plain,
% 16.17/10.65 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(2,plain,
% 16.17/10.65 ((ssList(V!48) & (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(3,plain,
% 16.17/10.65 ((ssList(W!49) & ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(4,plain,
% 16.17/10.65 (((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & (ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(5,plain,
% 16.17/10.65 ((ssItem(X3!51) & (ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(6,plain,
% 16.17/10.65 ((ssList(X4!52) & ((app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(7,plain,
% 16.17/10.65 (((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))) <=> ((app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(8,plain,
% 16.17/10.65 ((~(~ssList(X4!52))) <=> ssList(X4!52)),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(9,plain,
% 16.17/10.65 (((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssList(X4!52) & ((app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))),
% 16.17/10.65 inference(monotonicity,[status(thm)],[8, 7])).
% 16.17/10.65 tff(10,plain,
% 16.17/10.65 (((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> (ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.65 inference(transitivity,[status(thm)],[9, 6])).
% 16.17/10.65 tff(11,plain,
% 16.17/10.65 ((~(~ssItem(X3!51))) <=> ssItem(X3!51)),
% 16.17/10.65 inference(rewrite,[status(thm)],[])).
% 16.17/10.65 tff(12,plain,
% 16.17/10.65 (((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))) <=> (ssItem(X3!51) & (ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))),
% 16.17/10.66 inference(monotonicity,[status(thm)],[11, 10])).
% 16.17/10.66 tff(13,plain,
% 16.17/10.66 (((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))) <=> (ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.66 inference(transitivity,[status(thm)],[12, 5])).
% 16.17/10.66 tff(14,plain,
% 16.17/10.66 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 16.17/10.66 inference(rewrite,[status(thm)],[])).
% 16.17/10.66 tff(15,plain,
% 16.17/10.66 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 16.17/10.66 inference(rewrite,[status(thm)],[])).
% 16.17/10.66 tff(16,plain,
% 16.17/10.66 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 16.17/10.66 inference(rewrite,[status(thm)],[])).
% 16.17/10.66 tff(17,plain,
% 16.17/10.66 (((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))))) <=> ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & (ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))),
% 16.17/10.66 inference(monotonicity,[status(thm)],[16, 15, 14, 13])).
% 16.17/10.66 tff(18,plain,
% 16.17/10.66 (((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))))) <=> ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.17/10.66 inference(transitivity,[status(thm)],[17, 4])).
% 16.17/10.66 tff(19,plain,
% 16.17/10.66 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 16.17/10.66 inference(rewrite,[status(thm)],[])).
% 16.17/10.66 tff(20,plain,
% 16.17/10.66 (((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))))) <=> (ssList(W!49) & ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))),
% 16.20/10.66 inference(monotonicity,[status(thm)],[19, 18])).
% 16.20/10.66 tff(21,plain,
% 16.20/10.66 (((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))))) <=> (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.20/10.66 inference(transitivity,[status(thm)],[20, 3])).
% 16.20/10.66 tff(22,plain,
% 16.20/10.66 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 16.20/10.66 inference(rewrite,[status(thm)],[])).
% 16.20/10.66 tff(23,plain,
% 16.20/10.66 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))))))) <=> (ssList(V!48) & (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))),
% 16.20/10.66 inference(monotonicity,[status(thm)],[22, 21])).
% 16.20/10.66 tff(24,plain,
% 16.20/10.66 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))))))) <=> (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.20/10.66 inference(transitivity,[status(thm)],[23, 2])).
% 16.20/10.66 tff(25,plain,
% 16.20/10.66 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 16.20/10.66 inference(rewrite,[status(thm)],[])).
% 16.20/10.66 tff(26,plain,
% 16.20/10.66 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))),
% 16.20/10.66 inference(monotonicity,[status(thm)],[25, 24])).
% 16.20/10.66 tff(27,plain,
% 16.20/10.66 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ((~(~ssItem(X3!51))) & ((~(~ssList(X4!52))) & ((~(~(app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47))) & (~(~ssList(X5!53))) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.20/10.66 inference(transitivity,[status(thm)],[26, 1])).
% 16.20/10.66 tff(28,plain,
% 16.20/10.66 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6))))))))))))),
% 16.20/10.66 inference(rewrite,[status(thm)],[])).
% 16.20/10.66 tff(29,plain,
% 16.20/10.66 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W)) & ?[X2: $i] : (ssItem(X2) & (((~leq(Y, X2)) & memberP(X1, X2)) | ((~leq(X2, Y)) & memberP(Z, X2)))))))) | ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssList(X4) => ![X5: $i] : (ssList(X5) => ((~(app(app(X4, cons(X3, nil)), X5) = U)) | ![X6: $i] : (ssItem(X6) => (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6))))))))))))),
% 16.20/10.66 inference(rewrite,[status(thm)],[])).
% 16.20/10.66 tff(30,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W)) & ?[X2: $i] : (ssItem(X2) & (((~leq(Y, X2)) & memberP(X1, X2)) | ((~leq(X2, Y)) & memberP(Z, X2)))))))) | ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssList(X4) => ![X5: $i] : (ssList(X5) => ((~(app(app(X4, cons(X3, nil)), X5) = U)) | ![X6: $i] : (ssItem(X6) => (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 16.20/10.66 tff(31,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[30, 29])).
% 16.20/10.66 tff(32,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[31, 28])).
% 16.20/10.66 tff(33,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[32, 28])).
% 16.20/10.66 tff(34,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[33, 28])).
% 16.20/10.66 tff(35,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[34, 28])).
% 16.20/10.66 tff(36,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[35, 28])).
% 16.20/10.66 tff(37,plain,
% 16.20/10.66 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W) & ?[X2: $i] : (ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | ![X5: $i] : ((~(app(app(X4, cons(X3, nil)), X5) = U)) | (~ssList(X5)) | ![X6: $i] : ((~ssItem(X6)) | (((~memberP(X4, X6)) | leq(X6, X3)) & ((~memberP(X5, X6)) | leq(X3, X6)))))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[36, 28])).
% 16.20/10.66 tff(38,plain,
% 16.20/10.66 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) & ssItem(X3!51) & ssList(X4!52) & (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47) & ssList(X5!53) & (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[37, 27])).
% 16.20/10.66 tff(39,plain,
% 16.20/10.66 (U!47 = W!49),
% 16.20/10.66 inference(and_elim,[status(thm)],[38])).
% 16.20/10.66 tff(40,plain,
% 16.20/10.66 (app(app(X4!52, cons(X3!51, nil)), X5!53) = U!47),
% 16.20/10.66 inference(and_elim,[status(thm)],[38])).
% 16.20/10.66 tff(41,plain,
% 16.20/10.66 (app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49),
% 16.20/10.66 inference(transitivity,[status(thm)],[40, 39])).
% 16.20/10.66 tff(42,plain,
% 16.20/10.66 (ssItem(X3!51)),
% 16.20/10.66 inference(and_elim,[status(thm)],[38])).
% 16.20/10.66 tff(43,plain,
% 16.20/10.66 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))))),
% 16.20/10.66 inference(bind,[status(th)],[])).
% 16.20/10.66 tff(44,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))),
% 16.20/10.66 inference(quant_intro,[status(thm)],[43])).
% 16.20/10.66 tff(45,plain,
% 16.20/10.66 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))))),
% 16.20/10.66 inference(bind,[status(th)],[])).
% 16.20/10.66 tff(46,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))),
% 16.20/10.66 inference(quant_intro,[status(thm)],[45])).
% 16.20/10.66 tff(47,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))),
% 16.20/10.66 inference(transitivity,[status(thm)],[46, 44])).
% 16.20/10.66 tff(48,plain,
% 16.20/10.66 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2))))))))))),
% 16.20/10.66 inference(bind,[status(th)],[])).
% 16.20/10.66 tff(49,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2)))))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))),
% 16.20/10.66 inference(quant_intro,[status(thm)],[48])).
% 16.20/10.66 tff(50,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : (~(ssItem(X2) & (((~leq(X2, Y)) & memberP(Z, X2)) | ((~leq(Y, X2)) & memberP(X1, X2))))))))),
% 16.20/10.66 inference(and_elim,[status(thm)],[38])).
% 16.20/10.66 tff(51,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[50, 49])).
% 16.20/10.66 tff(52,plain,
% 16.20/10.66 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))),
% 16.20/10.66 inference(modus_ponens,[status(thm)],[51, 47])).
% 16.20/10.66 tff(53,plain,
% 16.20/10.66 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51)))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | (~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51)))))))))),
% 16.20/10.66 inference(rewrite,[status(thm)],[])).
% 16.20/10.66 tff(54,plain,
% 16.20/10.66 (((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, X3!51) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(X3!51, X2))))))))) <=> ((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51)))))))))),
% 16.20/10.66 inference(rewrite,[status(thm)],[])).
% 16.20/10.66 tff(55,plain,
% 16.20/10.66 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, X3!51) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(X3!51, X2)))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))))),
% 16.20/10.66 inference(monotonicity,[status(thm)],[54])).
% 16.20/10.66 tff(56,plain,
% 16.20/10.66 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, X3!51) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(X3!51, X2)))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | (~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51)))))))))),
% 16.20/10.66 inference(transitivity,[status(thm)],[55, 53])).
% 16.20/10.66 tff(57,plain,
% 16.20/10.66 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, X3!51) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(X3!51, X2)))))))))),
% 16.20/10.67 inference(quant_inst,[status(thm)],[])).
% 16.20/10.67 tff(58,plain,
% 16.20/10.67 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~(leq(X2, Y) | (~memberP(Z, X2)))) | (~((~memberP(X1, X2)) | leq(Y, X2)))))))))) | (~ssItem(X3!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))),
% 16.20/10.67 inference(modus_ponens,[status(thm)],[57, 56])).
% 16.20/10.67 tff(59,plain,
% 16.20/10.67 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))),
% 16.20/10.67 inference(unit_resolution,[status(thm)],[58, 52, 42])).
% 16.20/10.67 tff(60,plain,
% 16.20/10.67 (ssList(X4!52)),
% 16.20/10.67 inference(and_elim,[status(thm)],[38])).
% 16.20/10.67 tff(61,plain,
% 16.20/10.67 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))) | ((~ssList(X4!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51))))))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))) | (~ssList(X4!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51))))))))),
% 16.20/10.67 inference(rewrite,[status(thm)],[])).
% 16.20/10.67 tff(62,plain,
% 16.20/10.67 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))) | ((~ssList(X4!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51))))))))),
% 16.20/10.67 inference(quant_inst,[status(thm)],[])).
% 16.20/10.67 tff(63,plain,
% 16.20/10.67 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(Z, X2)) | leq(X2, X3!51))))))))) | (~ssList(X4!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))),
% 16.20/10.67 inference(modus_ponens,[status(thm)],[62, 61])).
% 16.20/10.67 tff(64,plain,
% 16.20/10.67 (![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))),
% 16.20/10.67 inference(unit_resolution,[status(thm)],[63, 60, 59])).
% 16.20/10.67 tff(65,plain,
% 16.20/10.67 (ssList(X5!53)),
% 16.20/10.67 inference(and_elim,[status(thm)],[38])).
% 16.20/10.67 tff(66,plain,
% 16.20/10.67 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | ((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2)))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | (~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2)))))))),
% 16.20/10.67 inference(rewrite,[status(thm)],[])).
% 16.20/10.67 tff(67,plain,
% 16.20/10.67 (((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X5!53, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51))))))) <=> ((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2)))))))),
% 16.20/10.67 inference(rewrite,[status(thm)],[])).
% 16.20/10.67 tff(68,plain,
% 16.20/10.67 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | ((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X5!53, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | ((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))))),
% 16.20/10.67 inference(monotonicity,[status(thm)],[67])).
% 16.20/10.67 tff(69,plain,
% 16.20/10.67 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | ((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X5!53, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | (~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2)))))))),
% 16.20/10.67 inference(transitivity,[status(thm)],[68, 66])).
% 16.20/10.67 tff(70,plain,
% 16.20/10.67 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | ((~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X5!53, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))),
% 16.20/10.67 inference(quant_inst,[status(thm)],[])).
% 16.20/10.67 tff(71,plain,
% 16.20/10.67 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(X4!52, cons(X3!51, nil)), X1) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X1, X2)) | leq(X3!51, X2))) | (~((~memberP(X4!52, X2)) | leq(X2, X3!51)))))))) | (~ssList(X5!53)) | (~(app(app(X4!52, cons(X3!51, nil)), X5!53) = W!49)) | ![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))),
% 16.20/10.67 inference(modus_ponens,[status(thm)],[70, 69])).
% 16.20/10.67 tff(72,plain,
% 16.20/10.67 (![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))),
% 16.20/10.67 inference(unit_resolution,[status(thm)],[71, 65, 64, 41])).
% 16.20/10.67 tff(73,plain,
% 16.20/10.67 (~((~ssItem(X6!54)) | (((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))),
% 16.20/10.67 inference(and_elim,[status(thm)],[38])).
% 16.20/10.67 tff(74,plain,
% 16.20/10.67 (ssItem(X6!54)),
% 16.20/10.67 inference(or_elim,[status(thm)],[73])).
% 16.20/10.67 tff(75,plain,
% 16.20/10.70 (((~![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))) | ((~ssItem(X6!54)) | (~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))) <=> ((~![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))) | (~ssItem(X6!54)) | (~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.20/10.70 inference(rewrite,[status(thm)],[])).
% 16.20/10.70 tff(76,plain,
% 16.20/10.70 ((~![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))) | ((~ssItem(X6!54)) | (~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.20/10.70 inference(quant_inst,[status(thm)],[])).
% 16.20/10.70 tff(77,plain,
% 16.20/10.70 ((~![X2: $i] : ((~ssItem(X2)) | (~((~((~memberP(X4!52, X2)) | leq(X2, X3!51))) | (~((~memberP(X5!53, X2)) | leq(X3!51, X2))))))) | (~ssItem(X6!54)) | (~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))),
% 16.20/10.70 inference(modus_ponens,[status(thm)],[76, 75])).
% 16.20/10.70 tff(78,plain,
% 16.20/10.70 (~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))),
% 16.20/10.70 inference(unit_resolution,[status(thm)],[77, 74, 72])).
% 16.20/10.70 tff(79,plain,
% 16.20/10.70 (((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))) | ((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))),
% 16.20/10.70 inference(tautology,[status(thm)],[])).
% 16.20/10.70 tff(80,plain,
% 16.20/10.70 ((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)),
% 16.20/10.70 inference(unit_resolution,[status(thm)],[79, 78])).
% 16.20/10.70 tff(81,plain,
% 16.20/10.70 (((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))) | ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))),
% 16.20/10.70 inference(tautology,[status(thm)],[])).
% 16.20/10.70 tff(82,plain,
% 16.20/10.70 ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)),
% 16.20/10.70 inference(unit_resolution,[status(thm)],[81, 78])).
% 16.20/10.70 tff(83,plain,
% 16.20/10.70 ((~(~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))) <=> ((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))),
% 16.20/10.70 inference(rewrite,[status(thm)],[])).
% 16.20/10.70 tff(84,plain,
% 16.20/10.70 ((((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))) <=> (~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))))),
% 16.20/10.70 inference(rewrite,[status(thm)],[])).
% 16.20/10.70 tff(85,plain,
% 16.20/10.70 ((~(((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))) <=> (~(~((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))))),
% 16.20/10.70 inference(monotonicity,[status(thm)],[84])).
% 16.20/10.70 tff(86,plain,
% 16.20/10.70 ((~(((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))) <=> ((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54))))),
% 16.20/10.70 inference(transitivity,[status(thm)],[85, 83])).
% 16.20/10.70 tff(87,plain,
% 16.20/10.70 (~(((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51)) & ((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))),
% 16.20/10.70 inference(or_elim,[status(thm)],[73])).
% 16.20/10.70 tff(88,plain,
% 16.20/10.70 ((~((~memberP(X4!52, X6!54)) | leq(X6!54, X3!51))) | (~((~memberP(X5!53, X6!54)) | leq(X3!51, X6!54)))),
% 16.20/10.70 inference(modus_ponens,[status(thm)],[87, 86])).
% 16.20/10.70 tff(89,plain,
% 16.20/10.70 ($false),
% 16.20/10.70 inference(unit_resolution,[status(thm)],[88, 82, 80])).
% 16.20/10.70 % SZS output end Proof
%------------------------------------------------------------------------------