TSTP Solution File: SWC185+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC185+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 11:55:58 EDT 2022
% Result : Theorem 1.58s 1.28s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC185+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 22:21:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.58/1.28 % SZS status Theorem
% 1.58/1.28 % SZS output start Proof
% 1.58/1.28 tff(memberP_type, type, (
% 1.58/1.28 memberP: ( $i * $i ) > $o)).
% 1.58/1.28 tff(tptp_fun_X2_51_type, type, (
% 1.58/1.28 tptp_fun_X2_51: $i)).
% 1.58/1.28 tff(tptp_fun_X3_52_type, type, (
% 1.58/1.28 tptp_fun_X3_52: $i)).
% 1.58/1.28 tff(tptp_fun_X4_53_type, type, (
% 1.58/1.28 tptp_fun_X4_53: $i)).
% 1.58/1.28 tff(tptp_fun_W_49_type, type, (
% 1.58/1.28 tptp_fun_W_49: $i)).
% 1.58/1.28 tff(app_type, type, (
% 1.58/1.28 app: ( $i * $i ) > $i)).
% 1.58/1.28 tff(cons_type, type, (
% 1.58/1.28 cons: ( $i * $i ) > $i)).
% 1.58/1.28 tff(nil_type, type, (
% 1.58/1.28 nil: $i)).
% 1.58/1.28 tff(tptp_fun_U_47_type, type, (
% 1.58/1.28 tptp_fun_U_47: $i)).
% 1.58/1.28 tff(ssList_type, type, (
% 1.58/1.28 ssList: $i > $o)).
% 1.58/1.28 tff(ssItem_type, type, (
% 1.58/1.28 ssItem: $i > $o)).
% 1.58/1.28 tff(tptp_fun_X_50_type, type, (
% 1.58/1.28 tptp_fun_X_50: $i)).
% 1.58/1.28 tff(tptp_fun_V_48_type, type, (
% 1.58/1.28 tptp_fun_V_48: $i)).
% 1.58/1.28 tff(1,plain,
% 1.58/1.28 ((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.28 inference(rewrite,[status(thm)],[])).
% 1.58/1.28 tff(2,plain,
% 1.58/1.28 ((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.28 inference(rewrite,[status(thm)],[])).
% 1.58/1.28 tff(3,plain,
% 1.58/1.28 ((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.28 inference(rewrite,[status(thm)],[])).
% 1.58/1.28 tff(4,plain,
% 1.58/1.28 (((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & (ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> ((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(5,plain,
% 1.58/1.29 ((ssItem(X2!51) & (ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> (ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(6,plain,
% 1.58/1.29 (((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))) <=> (ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(7,plain,
% 1.58/1.29 ((~(~ssItem(X2!51))) <=> ssItem(X2!51)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(8,plain,
% 1.58/1.29 (((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> (ssItem(X2!51) & (ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[7, 6])).
% 1.58/1.29 tff(9,plain,
% 1.58/1.29 (((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))) <=> (ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[8, 5])).
% 1.58/1.29 tff(10,plain,
% 1.58/1.29 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(11,plain,
% 1.58/1.29 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(12,plain,
% 1.58/1.29 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(13,plain,
% 1.58/1.29 (((~(~(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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))) <=> ((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & (ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[12, 11, 10, 9])).
% 1.58/1.29 tff(14,plain,
% 1.58/1.29 (((~(~(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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))) <=> ((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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[13, 4])).
% 1.58/1.29 tff(15,plain,
% 1.58/1.29 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(16,plain,
% 1.58/1.29 (((~(~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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[15, 14])).
% 1.58/1.29 tff(17,plain,
% 1.58/1.29 (((~(~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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[16, 3])).
% 1.58/1.29 tff(18,plain,
% 1.58/1.29 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(19,plain,
% 1.58/1.29 (((~(~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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[18, 17])).
% 1.58/1.29 tff(20,plain,
% 1.58/1.29 (((~(~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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[19, 2])).
% 1.58/1.29 tff(21,plain,
% 1.58/1.29 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(22,plain,
% 1.58/1.29 (((~(~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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[21, 20])).
% 1.58/1.29 tff(23,plain,
% 1.58/1.29 (((~(~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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ((~(~ssItem(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))))))) <=> (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[22, 1])).
% 1.58/1.29 tff(24,plain,
% 1.58/1.29 ((~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))) <=> (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4))))))))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(25,plain,
% 1.58/1.29 ((~![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)) & (memberP(Z, Y) | memberP(X1, Y)))))) | ![X2: $i] : (ssItem(X2) => ![X3: $i] : (ssList(X3) => ![X4: $i] : (ssList(X4) => ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))))))))))))) <=> (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4))))))))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(26,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)) & (memberP(Z, Y) | memberP(X1, Y)))))) | ![X2: $i] : (ssItem(X2) => ![X3: $i] : (ssList(X3) => ![X4: $i] : (ssList(X4) => ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 1.58/1.29 tff(27,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.58/1.29 tff(28,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.58/1.29 tff(29,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.58/1.29 tff(30,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[29, 24])).
% 1.58/1.29 tff(31,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[30, 24])).
% 1.58/1.29 tff(32,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.58/1.29 tff(33,plain,
% 1.58/1.29 (~![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) & (memberP(X1, Y) | memberP(Z, Y))))) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(app(X3, cons(X2, nil)), X4) = U)) | ((~memberP(X3, X2)) & (~memberP(X4, X2))) | (~ssList(X4)))))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[32, 24])).
% 1.58/1.29 tff(34,plain,
% 1.58/1.29 (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) & (memberP(X1, Y) | memberP(Z, Y)))))) & ssItem(X2!51) & ssList(X3!52) & (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[33, 23])).
% 1.58/1.29 tff(35,plain,
% 1.58/1.29 (U!47 = W!49),
% 1.58/1.29 inference(and_elim,[status(thm)],[34])).
% 1.58/1.29 tff(36,plain,
% 1.58/1.29 (~((~(app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47)) | ((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) | (~ssList(X4!53)))),
% 1.58/1.29 inference(and_elim,[status(thm)],[34])).
% 1.58/1.29 tff(37,plain,
% 1.58/1.29 (app(app(X3!52, cons(X2!51, nil)), X4!53) = U!47),
% 1.58/1.29 inference(or_elim,[status(thm)],[36])).
% 1.58/1.29 tff(38,plain,
% 1.58/1.29 (app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49),
% 1.58/1.29 inference(transitivity,[status(thm)],[37, 35])).
% 1.58/1.29 tff(39,plain,
% 1.58/1.29 (ssItem(X2!51)),
% 1.58/1.29 inference(and_elim,[status(thm)],[34])).
% 1.58/1.29 tff(40,plain,
% 1.58/1.29 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))))),
% 1.58/1.29 inference(bind,[status(th)],[])).
% 1.58/1.29 tff(41,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(quant_intro,[status(thm)],[40])).
% 1.58/1.29 tff(42,plain,
% 1.58/1.29 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))))),
% 1.58/1.29 inference(bind,[status(th)],[])).
% 1.58/1.29 tff(43,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(quant_intro,[status(thm)],[42])).
% 1.58/1.29 tff(44,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[43, 41])).
% 1.58/1.29 tff(45,plain,
% 1.58/1.29 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W!49) & (memberP(X1, Y) | memberP(Z, Y)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y)))))))),
% 1.58/1.29 inference(bind,[status(th)],[])).
% 1.58/1.29 tff(46,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W!49) & (memberP(X1, Y) | memberP(Z, Y)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(quant_intro,[status(thm)],[45])).
% 1.58/1.29 tff(47,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = W!49) & (memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(and_elim,[status(thm)],[34])).
% 1.58/1.29 tff(48,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.58/1.29 tff(49,plain,
% 1.58/1.29 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[48, 44])).
% 1.58/1.29 tff(50,plain,
% 1.58/1.29 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))) | ((~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))) | (~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51))))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(51,plain,
% 1.58/1.29 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))) | ((~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51))))))),
% 1.58/1.29 inference(quant_inst,[status(thm)],[])).
% 1.58/1.29 tff(52,plain,
% 1.58/1.29 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = W!49)) | (~(memberP(X1, Y) | memberP(Z, Y))))))) | (~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.58/1.29 tff(53,plain,
% 1.58/1.29 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))),
% 1.58/1.29 inference(unit_resolution,[status(thm)],[52, 49, 39])).
% 1.58/1.29 tff(54,plain,
% 1.58/1.29 (ssList(X3!52)),
% 1.58/1.29 inference(and_elim,[status(thm)],[34])).
% 1.58/1.29 tff(55,plain,
% 1.58/1.29 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | (~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(56,plain,
% 1.58/1.29 (((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))))) <=> ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49))))),
% 1.58/1.29 inference(rewrite,[status(thm)],[])).
% 1.58/1.29 tff(57,plain,
% 1.58/1.29 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51)))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[56])).
% 1.58/1.29 tff(58,plain,
% 1.58/1.29 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51)))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | (~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49))))),
% 1.58/1.30 inference(transitivity,[status(thm)],[57, 55])).
% 1.58/1.30 tff(59,plain,
% 1.58/1.30 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51)))))),
% 1.58/1.30 inference(quant_inst,[status(thm)],[])).
% 1.58/1.30 tff(60,plain,
% 1.58/1.30 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = W!49)) | (~(memberP(X1, X2!51) | memberP(Z, X2!51)))))) | (~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))),
% 1.58/1.30 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.58/1.30 tff(61,plain,
% 1.58/1.30 (![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))),
% 1.58/1.30 inference(unit_resolution,[status(thm)],[60, 54, 53])).
% 1.58/1.30 tff(62,plain,
% 1.58/1.30 (ssList(X4!53)),
% 1.58/1.30 inference(or_elim,[status(thm)],[36])).
% 1.58/1.30 tff(63,plain,
% 1.58/1.30 (((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | ((~ssList(X4!53)) | (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | (~ssList(X4!53)) | (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))),
% 1.58/1.30 inference(rewrite,[status(thm)],[])).
% 1.58/1.30 tff(64,plain,
% 1.58/1.30 (((~ssList(X4!53)) | (~(memberP(X4!53, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49))) <=> ((~ssList(X4!53)) | (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))),
% 1.58/1.30 inference(rewrite,[status(thm)],[])).
% 1.58/1.30 tff(65,plain,
% 1.58/1.30 (((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | ((~ssList(X4!53)) | (~(memberP(X4!53, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | ((~ssList(X4!53)) | (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49))))),
% 1.58/1.30 inference(monotonicity,[status(thm)],[64])).
% 1.58/1.30 tff(66,plain,
% 1.58/1.30 (((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | ((~ssList(X4!53)) | (~(memberP(X4!53, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | (~ssList(X4!53)) | (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))),
% 1.58/1.30 inference(transitivity,[status(thm)],[65, 63])).
% 1.58/1.30 tff(67,plain,
% 1.58/1.30 ((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | ((~ssList(X4!53)) | (~(memberP(X4!53, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49)))),
% 1.58/1.30 inference(quant_inst,[status(thm)],[])).
% 1.58/1.30 tff(68,plain,
% 1.58/1.30 ((~![X1: $i] : ((~ssList(X1)) | (~(memberP(X1, X2!51) | memberP(X3!52, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X1) = W!49)))) | (~ssList(X4!53)) | (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))) | (~(app(app(X3!52, cons(X2!51, nil)), X4!53) = W!49))),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.58/1.31 tff(69,plain,
% 1.58/1.31 (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[68, 62, 61, 38])).
% 1.58/1.31 tff(70,plain,
% 1.58/1.31 ((memberP(X3!52, X2!51) | memberP(X4!53, X2!51)) | (~memberP(X3!52, X2!51))),
% 1.58/1.31 inference(tautology,[status(thm)],[])).
% 1.58/1.31 tff(71,plain,
% 1.58/1.31 (~memberP(X3!52, X2!51)),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.58/1.31 tff(72,plain,
% 1.58/1.31 ((memberP(X3!52, X2!51) | memberP(X4!53, X2!51)) | (~memberP(X4!53, X2!51))),
% 1.58/1.31 inference(tautology,[status(thm)],[])).
% 1.58/1.31 tff(73,plain,
% 1.58/1.31 (~memberP(X4!53, X2!51)),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[72, 69])).
% 1.58/1.31 tff(74,plain,
% 1.58/1.31 ((~(~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51)))) <=> (memberP(X3!52, X2!51) | memberP(X4!53, X2!51))),
% 1.58/1.31 inference(rewrite,[status(thm)],[])).
% 1.58/1.31 tff(75,plain,
% 1.58/1.31 (((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51))) <=> (~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51)))),
% 1.58/1.31 inference(rewrite,[status(thm)],[])).
% 1.58/1.31 tff(76,plain,
% 1.58/1.31 ((~((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51)))) <=> (~(~(memberP(X3!52, X2!51) | memberP(X4!53, X2!51))))),
% 1.58/1.31 inference(monotonicity,[status(thm)],[75])).
% 1.58/1.31 tff(77,plain,
% 1.58/1.31 ((~((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51)))) <=> (memberP(X3!52, X2!51) | memberP(X4!53, X2!51))),
% 1.58/1.31 inference(transitivity,[status(thm)],[76, 74])).
% 1.58/1.31 tff(78,plain,
% 1.58/1.31 (~((~memberP(X3!52, X2!51)) & (~memberP(X4!53, X2!51)))),
% 1.58/1.31 inference(or_elim,[status(thm)],[36])).
% 1.58/1.31 tff(79,plain,
% 1.58/1.31 (memberP(X3!52, X2!51) | memberP(X4!53, X2!51)),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.58/1.31 tff(80,plain,
% 1.58/1.31 ($false),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[79, 73, 71])).
% 1.58/1.31 % SZS output end Proof
%------------------------------------------------------------------------------