TSTP Solution File: SWC189+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC189+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 11:55:59 EDT 2022
% Result : Theorem 17.33s 11.43s
% Output : Proof 17.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC189+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 22:24:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 17.33/11.43 % SZS status Theorem
% 17.33/11.43 % SZS output start Proof
% 17.33/11.43 tff(tptp_fun_W_49_type, type, (
% 17.33/11.43 tptp_fun_W_49: $i)).
% 17.33/11.43 tff(app_type, type, (
% 17.33/11.43 app: ( $i * $i ) > $i)).
% 17.33/11.43 tff(tptp_fun_X6_54_type, type, (
% 17.33/11.43 tptp_fun_X6_54: $i)).
% 17.33/11.43 tff(cons_type, type, (
% 17.33/11.43 cons: ( $i * $i ) > $i)).
% 17.33/11.43 tff(nil_type, type, (
% 17.33/11.43 nil: $i)).
% 17.33/11.43 tff(tptp_fun_X4_52_type, type, (
% 17.33/11.43 tptp_fun_X4_52: $i)).
% 17.33/11.43 tff(tptp_fun_X3_51_type, type, (
% 17.33/11.43 tptp_fun_X3_51: $i)).
% 17.33/11.43 tff(tptp_fun_X5_53_type, type, (
% 17.33/11.43 tptp_fun_X5_53: $i)).
% 17.33/11.43 tff(tptp_fun_U_47_type, type, (
% 17.33/11.43 tptp_fun_U_47: $i)).
% 17.33/11.43 tff(ssList_type, type, (
% 17.33/11.43 ssList: $i > $o)).
% 17.33/11.43 tff(ssItem_type, type, (
% 17.33/11.43 ssItem: $i > $o)).
% 17.33/11.43 tff(tptp_fun_X_50_type, type, (
% 17.33/11.43 tptp_fun_X_50: $i)).
% 17.33/11.43 tff(tptp_fun_V_48_type, type, (
% 17.33/11.43 tptp_fun_V_48: $i)).
% 17.33/11.43 tff(1,plain,
% 17.33/11.43 ((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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(2,plain,
% 17.33/11.43 ((ssList(V!48) & (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(3,plain,
% 17.33/11.43 ((ssList(W!49) & ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))) <=> (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(4,plain,
% 17.33/11.43 (((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & (ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))) <=> ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(5,plain,
% 17.33/11.43 ((ssItem(X3!51) & (ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))) <=> (ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(6,plain,
% 17.33/11.43 ((ssItem(X4!52) & (ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))) <=> (ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(7,plain,
% 17.33/11.43 (((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))) <=> (ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(8,plain,
% 17.33/11.43 ((~(~ssItem(X4!52))) <=> ssItem(X4!52)),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(9,plain,
% 17.33/11.43 (((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))) <=> (ssItem(X4!52) & (ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))),
% 17.33/11.43 inference(monotonicity,[status(thm)],[8, 7])).
% 17.33/11.43 tff(10,plain,
% 17.33/11.43 (((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))) <=> (ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(transitivity,[status(thm)],[9, 6])).
% 17.33/11.43 tff(11,plain,
% 17.33/11.43 ((~(~ssItem(X3!51))) <=> ssItem(X3!51)),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(12,plain,
% 17.33/11.43 (((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))) <=> (ssItem(X3!51) & (ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))),
% 17.33/11.43 inference(monotonicity,[status(thm)],[11, 10])).
% 17.33/11.43 tff(13,plain,
% 17.33/11.43 (((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))) <=> (ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.43 inference(transitivity,[status(thm)],[12, 5])).
% 17.33/11.43 tff(14,plain,
% 17.33/11.43 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(15,plain,
% 17.33/11.43 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(16,plain,
% 17.33/11.43 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 17.33/11.43 inference(rewrite,[status(thm)],[])).
% 17.33/11.43 tff(17,plain,
% 17.33/11.43 (((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))))) <=> ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & (ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))),
% 17.33/11.44 inference(monotonicity,[status(thm)],[16, 15, 14, 13])).
% 17.33/11.44 tff(18,plain,
% 17.33/11.44 (((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))))) <=> ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.44 inference(transitivity,[status(thm)],[17, 4])).
% 17.33/11.44 tff(19,plain,
% 17.33/11.44 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(20,plain,
% 17.33/11.44 (((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))))) <=> (ssList(W!49) & ((V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))),
% 17.33/11.44 inference(monotonicity,[status(thm)],[19, 18])).
% 17.33/11.44 tff(21,plain,
% 17.33/11.44 (((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))))) <=> (ssList(W!49) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.44 inference(transitivity,[status(thm)],[20, 3])).
% 17.33/11.44 tff(22,plain,
% 17.33/11.44 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(23,plain,
% 17.33/11.44 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))),
% 17.33/11.44 inference(monotonicity,[status(thm)],[22, 21])).
% 17.33/11.44 tff(24,plain,
% 17.33/11.44 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.44 inference(transitivity,[status(thm)],[23, 2])).
% 17.33/11.44 tff(25,plain,
% 17.33/11.44 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(26,plain,
% 17.33/11.44 (((~(~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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))))),
% 17.33/11.44 inference(monotonicity,[status(thm)],[25, 24])).
% 17.33/11.44 tff(27,plain,
% 17.33/11.44 (((~(~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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ((~(~ssItem(X3!51))) & ((~(~ssItem(X4!52))) & ((~(~ssList(X5!53))) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))))),
% 17.33/11.44 inference(transitivity,[status(thm)],[26, 1])).
% 17.33/11.44 tff(28,plain,
% 17.33/11.44 ((~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6)))))))))))),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(29,plain,
% 17.33/11.44 ((~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : ((ssList(X2) & (~(Y = Z))) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W)))))) | ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssItem(X4) => ![X5: $i] : (ssList(X5) => ![X6: $i] : (ssList(X6) => ((~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (X3 = 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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6)))))))))))),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : ((ssList(X2) & (~(Y = Z))) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W)))))) | ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssItem(X4) => ![X5: $i] : (ssList(X5) => ![X6: $i] : (ssList(X6) => ((~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (X3 = X4)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 17.33/11.44 tff(31,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 17.33/11.44 tff(32,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[31, 28])).
% 17.33/11.44 tff(33,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[32, 28])).
% 17.33/11.44 tff(34,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[33, 28])).
% 17.33/11.44 tff(35,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[34, 28])).
% 17.33/11.44 tff(36,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[35, 28])).
% 17.33/11.44 tff(37,plain,
% 17.33/11.44 (~![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] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W))))) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (~ssList(X6))))))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[36, 28])).
% 17.33/11.44 tff(38,plain,
% 17.33/11.44 (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] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) & ssItem(X3!51) & ssItem(X4!52) & ssList(X5!53) & (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[37, 27])).
% 17.33/11.44 tff(39,plain,
% 17.33/11.44 (U!47 = W!49),
% 17.33/11.44 inference(and_elim,[status(thm)],[38])).
% 17.33/11.44 tff(40,plain,
% 17.33/11.44 (~((X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47)) | (~ssList(X6!54)))),
% 17.33/11.44 inference(and_elim,[status(thm)],[38])).
% 17.33/11.44 tff(41,plain,
% 17.33/11.44 (app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = U!47),
% 17.33/11.44 inference(or_elim,[status(thm)],[40])).
% 17.33/11.44 tff(42,plain,
% 17.33/11.44 (app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49),
% 17.33/11.44 inference(transitivity,[status(thm)],[41, 39])).
% 17.33/11.44 tff(43,plain,
% 17.33/11.44 (ssItem(X3!51)),
% 17.33/11.44 inference(and_elim,[status(thm)],[38])).
% 17.33/11.44 tff(44,plain,
% 17.33/11.44 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))))),
% 17.33/11.44 inference(bind,[status(th)],[])).
% 17.33/11.44 tff(45,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(quant_intro,[status(thm)],[44])).
% 17.33/11.44 tff(46,plain,
% 17.33/11.44 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))))),
% 17.33/11.44 inference(bind,[status(th)],[])).
% 17.33/11.44 tff(47,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(quant_intro,[status(thm)],[46])).
% 17.33/11.44 tff(48,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(transitivity,[status(thm)],[47, 45])).
% 17.33/11.44 tff(49,plain,
% 17.33/11.44 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))))),
% 17.33/11.44 inference(bind,[status(th)],[])).
% 17.33/11.44 tff(50,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(quant_intro,[status(thm)],[49])).
% 17.33/11.44 tff(51,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(and_elim,[status(thm)],[38])).
% 17.33/11.44 tff(52,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 17.33/11.44 tff(53,plain,
% 17.33/11.44 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[52, 48])).
% 17.33/11.44 tff(54,plain,
% 17.33/11.44 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | (~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(55,plain,
% 17.33/11.44 (((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!51 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))) <=> ((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(56,plain,
% 17.33/11.44 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!51 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))))),
% 17.33/11.44 inference(monotonicity,[status(thm)],[55])).
% 17.33/11.44 tff(57,plain,
% 17.33/11.44 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!51 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | (~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(transitivity,[status(thm)],[56, 54])).
% 17.33/11.44 tff(58,plain,
% 17.33/11.44 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | ((~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!51 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49))))))),
% 17.33/11.44 inference(quant_inst,[status(thm)],[])).
% 17.33/11.44 tff(59,plain,
% 17.33/11.44 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W!49))))))) | (~ssItem(X3!51)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))),
% 17.33/11.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 17.33/11.44 tff(60,plain,
% 17.33/11.44 (![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))),
% 17.33/11.44 inference(unit_resolution,[status(thm)],[59, 53, 43])).
% 17.33/11.44 tff(61,plain,
% 17.33/11.44 (ssItem(X4!52)),
% 17.33/11.44 inference(and_elim,[status(thm)],[38])).
% 17.33/11.44 tff(62,plain,
% 17.33/11.44 (((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))) | ((~ssItem(X4!52)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))))) <=> ((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))) | (~ssItem(X4!52)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))))),
% 17.33/11.44 inference(rewrite,[status(thm)],[])).
% 17.33/11.44 tff(63,plain,
% 17.33/11.44 ((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))) | ((~ssItem(X4!52)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))))),
% 17.33/11.45 inference(quant_inst,[status(thm)],[])).
% 17.33/11.45 tff(64,plain,
% 17.33/11.45 ((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = Z) | (~(app(app(app(X1, cons(X3!51, nil)), cons(Z, nil)), X2) = W!49)))))) | (~ssItem(X4!52)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))),
% 17.33/11.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 17.33/11.45 tff(65,plain,
% 17.33/11.45 (![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))),
% 17.33/11.45 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 17.33/11.45 tff(66,plain,
% 17.33/11.45 (ssList(X5!53)),
% 17.33/11.45 inference(and_elim,[status(thm)],[38])).
% 17.33/11.45 tff(67,plain,
% 17.33/11.45 (((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))) | ((~ssList(X5!53)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))) <=> ((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))) | (~ssList(X5!53)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))),
% 17.33/11.45 inference(rewrite,[status(thm)],[])).
% 17.33/11.45 tff(68,plain,
% 17.33/11.45 ((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))) | ((~ssList(X5!53)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))),
% 17.33/11.45 inference(quant_inst,[status(thm)],[])).
% 17.33/11.45 tff(69,plain,
% 17.33/11.45 ((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X1, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49))))) | (~ssList(X5!53)) | ![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))),
% 17.33/11.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 17.33/11.45 tff(70,plain,
% 17.33/11.45 (![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))),
% 17.33/11.45 inference(unit_resolution,[status(thm)],[69, 66, 65])).
% 17.33/11.45 tff(71,plain,
% 17.33/11.45 (ssList(X6!54)),
% 17.33/11.45 inference(or_elim,[status(thm)],[40])).
% 17.33/11.45 tff(72,plain,
% 17.33/11.45 (~(X3!51 = X4!52)),
% 17.33/11.45 inference(or_elim,[status(thm)],[40])).
% 17.33/11.45 tff(73,plain,
% 17.33/11.45 (((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | ((X3!51 = X4!52) | (~ssList(X6!54)) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))) <=> ((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | (X3!51 = X4!52) | (~ssList(X6!54)) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))),
% 17.33/11.45 inference(rewrite,[status(thm)],[])).
% 17.33/11.45 tff(74,plain,
% 17.33/11.45 (((~ssList(X6!54)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49))) <=> ((X3!51 = X4!52) | (~ssList(X6!54)) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))),
% 17.33/11.45 inference(rewrite,[status(thm)],[])).
% 17.33/11.45 tff(75,plain,
% 17.33/11.45 (((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | ((~ssList(X6!54)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))) <=> ((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | ((X3!51 = X4!52) | (~ssList(X6!54)) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49))))),
% 17.33/11.49 inference(monotonicity,[status(thm)],[74])).
% 17.33/11.49 tff(76,plain,
% 17.33/11.49 (((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | ((~ssList(X6!54)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))) <=> ((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | (X3!51 = X4!52) | (~ssList(X6!54)) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))),
% 17.33/11.49 inference(transitivity,[status(thm)],[75, 73])).
% 17.33/11.49 tff(77,plain,
% 17.33/11.49 ((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | ((~ssList(X6!54)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49)))),
% 17.33/11.49 inference(quant_inst,[status(thm)],[])).
% 17.33/11.49 tff(78,plain,
% 17.33/11.49 ((~![X2: $i] : ((~ssList(X2)) | (X3!51 = X4!52) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X2) = W!49)))) | (X3!51 = X4!52) | (~ssList(X6!54)) | (~(app(app(app(X5!53, cons(X3!51, nil)), cons(X4!52, nil)), X6!54) = W!49))),
% 17.33/11.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 17.33/11.49 tff(79,plain,
% 17.33/11.49 ($false),
% 17.33/11.49 inference(unit_resolution,[status(thm)],[78, 72, 71, 70, 42])).
% 17.33/11.49 % SZS output end Proof
%------------------------------------------------------------------------------