TSTP Solution File: SWC006+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC006+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 11:54:35 EDT 2022
% Result : Theorem 2.32s 1.76s
% Output : Proof 2.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC006+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.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 20:00:54 EDT 2022
% 0.12/0.33 % 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.
% 2.32/1.76 % SZS status Theorem
% 2.32/1.76 % SZS output start Proof
% 2.32/1.76 tff(tptp_fun_V_48_type, type, (
% 2.32/1.76 tptp_fun_V_48: $i)).
% 2.32/1.76 tff(app_type, type, (
% 2.32/1.76 app: ( $i * $i ) > $i)).
% 2.32/1.76 tff(tptp_fun_X4_53_type, type, (
% 2.32/1.76 tptp_fun_X4_53: $i)).
% 2.32/1.76 tff(tptp_fun_X3_52_type, type, (
% 2.32/1.76 tptp_fun_X3_52: $i)).
% 2.32/1.76 tff(tptp_fun_X2_51_type, type, (
% 2.32/1.76 tptp_fun_X2_51: $i)).
% 2.32/1.76 tff(tptp_fun_X_50_type, type, (
% 2.32/1.76 tptp_fun_X_50: $i)).
% 2.32/1.76 tff(ssList_type, type, (
% 2.32/1.76 ssList: $i > $o)).
% 2.32/1.76 tff(tptp_fun_W_49_type, type, (
% 2.32/1.76 tptp_fun_W_49: $i)).
% 2.32/1.76 tff(tptp_fun_U_47_type, type, (
% 2.32/1.76 tptp_fun_U_47: $i)).
% 2.32/1.76 tff(1,plain,
% 2.32/1.76 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(2,plain,
% 2.32/1.76 ((ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(3,plain,
% 2.32/1.76 ((ssList(W!49) & ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(4,plain,
% 2.32/1.76 (((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & (ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(5,plain,
% 2.32/1.76 ((ssList(X2!51) & (ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> (ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(6,plain,
% 2.32/1.76 (((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))) <=> (ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(7,plain,
% 2.32/1.76 ((~(~ssList(X2!51))) <=> ssList(X2!51)),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(8,plain,
% 2.32/1.76 (((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> (ssList(X2!51) & (ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))),
% 2.32/1.76 inference(monotonicity,[status(thm)],[7, 6])).
% 2.32/1.76 tff(9,plain,
% 2.32/1.76 (((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))) <=> (ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(transitivity,[status(thm)],[8, 5])).
% 2.32/1.76 tff(10,plain,
% 2.32/1.76 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(11,plain,
% 2.32/1.76 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(12,plain,
% 2.32/1.76 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(13,plain,
% 2.32/1.76 (((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))) <=> ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & (ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))),
% 2.32/1.76 inference(monotonicity,[status(thm)],[12, 11, 10, 9])).
% 2.32/1.76 tff(14,plain,
% 2.32/1.76 (((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))) <=> ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.76 inference(transitivity,[status(thm)],[13, 4])).
% 2.32/1.76 tff(15,plain,
% 2.32/1.76 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 2.32/1.76 inference(rewrite,[status(thm)],[])).
% 2.32/1.76 tff(16,plain,
% 2.32/1.76 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))))) <=> (ssList(W!49) & ((U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))),
% 2.32/1.76 inference(monotonicity,[status(thm)],[15, 14])).
% 2.32/1.76 tff(17,plain,
% 2.32/1.76 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))))) <=> (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.77 inference(transitivity,[status(thm)],[16, 3])).
% 2.32/1.77 tff(18,plain,
% 2.32/1.77 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 2.32/1.77 inference(rewrite,[status(thm)],[])).
% 2.32/1.77 tff(19,plain,
% 2.32/1.77 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))),
% 2.32/1.77 inference(monotonicity,[status(thm)],[18, 17])).
% 2.32/1.77 tff(20,plain,
% 2.32/1.77 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.77 inference(transitivity,[status(thm)],[19, 2])).
% 2.32/1.77 tff(21,plain,
% 2.32/1.77 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 2.32/1.77 inference(rewrite,[status(thm)],[])).
% 2.32/1.77 tff(22,plain,
% 2.32/1.77 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))))),
% 2.32/1.77 inference(monotonicity,[status(thm)],[21, 20])).
% 2.32/1.77 tff(23,plain,
% 2.32/1.77 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~ssList(X2!51))) & ((~(~ssList(X3!52))) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))))),
% 2.32/1.77 inference(transitivity,[status(thm)],[22, 1])).
% 2.32/1.77 tff(24,plain,
% 2.32/1.77 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4))))))))))),
% 2.32/1.77 inference(rewrite,[status(thm)],[])).
% 2.32/1.77 tff(25,plain,
% 2.32/1.77 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (((((~ssList(X)) | (~(V = X))) | (~(U = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ![X2: $i] : (ssList(X2) => ![X3: $i] : (ssList(X3) => ![X4: $i] : (((~ssList(X4)) | (~(app(app(X2, X3), X4) = X))) | (~(app(X2, X4) = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4))))))))))),
% 2.32/1.77 inference(rewrite,[status(thm)],[])).
% 2.32/1.77 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] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ![X2: $i] : (ssList(X2) => ![X3: $i] : (ssList(X3) => ![X4: $i] : (((~ssList(X4)) | (~(app(app(X2, X3), X4) = X))) | (~(app(X2, X4) = W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 2.32/1.77 tff(27,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[26, 25])).
% 2.32/1.77 tff(28,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[27, 24])).
% 2.32/1.77 tff(29,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.32/1.77 tff(30,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[29, 24])).
% 2.32/1.77 tff(31,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[30, 24])).
% 2.32/1.77 tff(32,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[31, 24])).
% 2.32/1.77 tff(33,plain,
% 2.32/1.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~ssList(X2)) | ![X3: $i] : ((~ssList(X3)) | ![X4: $i] : ((~(app(X2, X4) = W)) | (~(app(app(X2, X3), X4) = X)) | (~ssList(X4)))))))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[32, 24])).
% 2.32/1.77 tff(34,plain,
% 2.32/1.77 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ssList(X2!51) & ssList(X3!52) & (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[33, 23])).
% 2.32/1.77 tff(35,plain,
% 2.32/1.77 (V!48 = X!50),
% 2.32/1.77 inference(and_elim,[status(thm)],[34])).
% 2.32/1.77 tff(36,plain,
% 2.32/1.77 (X!50 = V!48),
% 2.32/1.77 inference(symmetry,[status(thm)],[35])).
% 2.32/1.77 tff(37,plain,
% 2.32/1.77 (~((~(app(X2!51, X4!53) = W!49)) | (~(app(app(X2!51, X3!52), X4!53) = X!50)) | (~ssList(X4!53)))),
% 2.32/1.77 inference(and_elim,[status(thm)],[34])).
% 2.32/1.77 tff(38,plain,
% 2.32/1.77 (app(app(X2!51, X3!52), X4!53) = X!50),
% 2.32/1.77 inference(or_elim,[status(thm)],[37])).
% 2.32/1.77 tff(39,plain,
% 2.32/1.77 (app(app(X2!51, X3!52), X4!53) = V!48),
% 2.32/1.77 inference(transitivity,[status(thm)],[38, 36])).
% 2.32/1.77 tff(40,plain,
% 2.32/1.77 (U!47 = W!49),
% 2.32/1.77 inference(and_elim,[status(thm)],[34])).
% 2.32/1.77 tff(41,plain,
% 2.32/1.77 (W!49 = U!47),
% 2.32/1.77 inference(symmetry,[status(thm)],[40])).
% 2.32/1.77 tff(42,plain,
% 2.32/1.77 (app(X2!51, X4!53) = W!49),
% 2.32/1.77 inference(or_elim,[status(thm)],[37])).
% 2.32/1.77 tff(43,plain,
% 2.32/1.77 (app(X2!51, X4!53) = U!47),
% 2.32/1.77 inference(transitivity,[status(thm)],[42, 41])).
% 2.32/1.77 tff(44,plain,
% 2.32/1.77 (ssList(X2!51)),
% 2.32/1.77 inference(and_elim,[status(thm)],[34])).
% 2.32/1.77 tff(45,plain,
% 2.32/1.77 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 2.32/1.77 inference(bind,[status(th)],[])).
% 2.32/1.77 tff(46,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(quant_intro,[status(thm)],[45])).
% 2.32/1.77 tff(47,plain,
% 2.32/1.77 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 2.32/1.77 inference(bind,[status(th)],[])).
% 2.32/1.77 tff(48,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(quant_intro,[status(thm)],[47])).
% 2.32/1.77 tff(49,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(transitivity,[status(thm)],[48, 46])).
% 2.32/1.77 tff(50,plain,
% 2.32/1.77 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 2.32/1.77 inference(bind,[status(th)],[])).
% 2.32/1.77 tff(51,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(quant_intro,[status(thm)],[50])).
% 2.32/1.77 tff(52,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(and_elim,[status(thm)],[34])).
% 2.32/1.77 tff(53,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[52, 51])).
% 2.32/1.77 tff(54,plain,
% 2.32/1.77 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 2.32/1.77 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.32/1.77 tff(55,plain,
% 2.32/1.77 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48)))))),
% 2.32/1.77 inference(rewrite,[status(thm)],[])).
% 2.32/1.77 tff(56,plain,
% 2.32/1.77 (((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X2!51, Z), X1) = V!48)) | (~(app(X2!51, X1) = U!47))))) <=> ((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48)))))),
% 2.32/1.77 inference(rewrite,[status(thm)],[])).
% 2.32/1.77 tff(57,plain,
% 2.32/1.77 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X2!51, Z), X1) = V!48)) | (~(app(X2!51, X1) = U!47)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))))),
% 2.32/1.77 inference(monotonicity,[status(thm)],[56])).
% 2.32/1.77 tff(58,plain,
% 2.32/1.77 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X2!51, Z), X1) = V!48)) | (~(app(X2!51, X1) = U!47)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48)))))),
% 2.32/1.77 inference(transitivity,[status(thm)],[57, 55])).
% 2.32/1.77 tff(59,plain,
% 2.32/1.77 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(X2!51, Z), X1) = V!48)) | (~(app(X2!51, X1) = U!47)))))),
% 2.32/1.78 inference(quant_inst,[status(thm)],[])).
% 2.32/1.78 tff(60,plain,
% 2.32/1.78 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))),
% 2.32/1.78 inference(modus_ponens,[status(thm)],[59, 58])).
% 2.32/1.78 tff(61,plain,
% 2.32/1.78 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))),
% 2.32/1.78 inference(unit_resolution,[status(thm)],[60, 54, 44])).
% 2.32/1.78 tff(62,plain,
% 2.32/1.78 (ssList(X3!52)),
% 2.32/1.78 inference(and_elim,[status(thm)],[34])).
% 2.32/1.78 tff(63,plain,
% 2.32/1.78 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))) | (~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48))))),
% 2.32/1.78 inference(rewrite,[status(thm)],[])).
% 2.32/1.78 tff(64,plain,
% 2.32/1.78 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))) | ((~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48))))),
% 2.32/1.78 inference(quant_inst,[status(thm)],[])).
% 2.32/1.78 tff(65,plain,
% 2.32/1.78 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, Z), X1) = V!48))))) | (~ssList(X3!52)) | ![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48)))),
% 2.32/1.78 inference(modus_ponens,[status(thm)],[64, 63])).
% 2.32/1.78 tff(66,plain,
% 2.32/1.78 (![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48)))),
% 2.32/1.78 inference(unit_resolution,[status(thm)],[65, 62, 61])).
% 2.32/1.78 tff(67,plain,
% 2.32/1.78 (ssList(X4!53)),
% 2.32/1.78 inference(or_elim,[status(thm)],[37])).
% 2.32/1.78 tff(68,plain,
% 2.32/1.78 (((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48)))) | ((~ssList(X4!53)) | (~(app(X2!51, X4!53) = U!47)) | (~(app(app(X2!51, X3!52), X4!53) = V!48)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48)))) | (~ssList(X4!53)) | (~(app(X2!51, X4!53) = U!47)) | (~(app(app(X2!51, X3!52), X4!53) = V!48)))),
% 2.32/1.78 inference(rewrite,[status(thm)],[])).
% 2.32/1.78 tff(69,plain,
% 2.32/1.78 ((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48)))) | ((~ssList(X4!53)) | (~(app(X2!51, X4!53) = U!47)) | (~(app(app(X2!51, X3!52), X4!53) = V!48)))),
% 2.32/1.78 inference(quant_inst,[status(thm)],[])).
% 2.32/1.78 tff(70,plain,
% 2.32/1.78 ((~![X1: $i] : ((~ssList(X1)) | (~(app(X2!51, X1) = U!47)) | (~(app(app(X2!51, X3!52), X1) = V!48)))) | (~ssList(X4!53)) | (~(app(X2!51, X4!53) = U!47)) | (~(app(app(X2!51, X3!52), X4!53) = V!48))),
% 2.32/1.78 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.32/1.78 tff(71,plain,
% 2.32/1.78 ($false),
% 2.32/1.78 inference(unit_resolution,[status(thm)],[70, 67, 66, 43, 39])).
% 2.32/1.78 % SZS output end Proof
%------------------------------------------------------------------------------