TSTP Solution File: SWC218+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC218+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:56:13 EDT 2022
% Result : Theorem 10.31s 6.87s
% Output : Proof 10.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC218+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 22:40:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 10.31/6.87 % SZS status Theorem
% 10.31/6.87 % SZS output start Proof
% 10.31/6.87 tff(app_type, type, (
% 10.31/6.87 app: ( $i * $i ) > $i)).
% 10.31/6.87 tff(cons_type, type, (
% 10.31/6.87 cons: ( $i * $i ) > $i)).
% 10.31/6.87 tff(nil_type, type, (
% 10.31/6.87 nil: $i)).
% 10.31/6.87 tff(tptp_fun_X1_53_type, type, (
% 10.31/6.87 tptp_fun_X1_53: $i)).
% 10.31/6.87 tff(tptp_fun_Y_51_type, type, (
% 10.31/6.87 tptp_fun_Y_51: $i)).
% 10.31/6.87 tff(tptp_fun_Z_52_type, type, (
% 10.31/6.87 tptp_fun_Z_52: $i)).
% 10.31/6.87 tff(tptp_fun_W_49_type, type, (
% 10.31/6.87 tptp_fun_W_49: $i)).
% 10.31/6.87 tff(ssItem_type, type, (
% 10.31/6.87 ssItem: $i > $o)).
% 10.31/6.87 tff(ssList_type, type, (
% 10.31/6.87 ssList: $i > $o)).
% 10.31/6.87 tff(tptp_fun_X_50_type, type, (
% 10.31/6.87 tptp_fun_X_50: $i)).
% 10.31/6.87 tff(tptp_fun_U_47_type, type, (
% 10.31/6.87 tptp_fun_U_47: $i)).
% 10.31/6.87 tff(tptp_fun_V_48_type, type, (
% 10.31/6.87 tptp_fun_V_48: $i)).
% 10.31/6.87 tff(neq_type, type, (
% 10.31/6.87 neq: ( $i * $i ) > $o)).
% 10.31/6.87 tff(1,plain,
% 10.31/6.87 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(2,plain,
% 10.31/6.87 ((ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(3,plain,
% 10.31/6.87 ((ssList(W!49) & ((~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(4,plain,
% 10.31/6.87 (((~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> ((~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(5,plain,
% 10.31/6.87 ((ssList(Y!51) & ((app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> (ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(6,plain,
% 10.31/6.87 (((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))) <=> ((app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(7,plain,
% 10.31/6.87 ((~(~ssList(Y!51))) <=> ssList(Y!51)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(8,plain,
% 10.31/6.87 (((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> (ssList(Y!51) & ((app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))),
% 10.31/6.87 inference(monotonicity,[status(thm)],[7, 6])).
% 10.31/6.87 tff(9,plain,
% 10.31/6.87 (((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))) <=> (ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(transitivity,[status(thm)],[8, 5])).
% 10.31/6.87 tff(10,plain,
% 10.31/6.87 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(11,plain,
% 10.31/6.87 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(12,plain,
% 10.31/6.87 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(13,plain,
% 10.31/6.87 (((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))) <=> ((~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))),
% 10.31/6.87 inference(monotonicity,[status(thm)],[12, 11, 10, 9])).
% 10.31/6.87 tff(14,plain,
% 10.31/6.87 (((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))) <=> ((~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(transitivity,[status(thm)],[13, 4])).
% 10.31/6.87 tff(15,plain,
% 10.31/6.87 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(16,plain,
% 10.31/6.87 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))))) <=> (ssList(W!49) & ((~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))),
% 10.31/6.87 inference(monotonicity,[status(thm)],[15, 14])).
% 10.31/6.87 tff(17,plain,
% 10.31/6.87 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(transitivity,[status(thm)],[16, 3])).
% 10.31/6.87 tff(18,plain,
% 10.31/6.87 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(19,plain,
% 10.31/6.87 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))),
% 10.31/6.87 inference(monotonicity,[status(thm)],[18, 17])).
% 10.31/6.87 tff(20,plain,
% 10.31/6.87 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(transitivity,[status(thm)],[19, 2])).
% 10.31/6.87 tff(21,plain,
% 10.31/6.87 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(22,plain,
% 10.31/6.87 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))))),
% 10.31/6.87 inference(monotonicity,[status(thm)],[21, 20])).
% 10.31/6.87 tff(23,plain,
% 10.31/6.87 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(Y!51, Z!52) = X!50))) & (~(~ssList(Z!52))) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))))),
% 10.31/6.87 inference(transitivity,[status(thm)],[22, 1])).
% 10.31/6.87 tff(24,plain,
% 10.31/6.87 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W))))))))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 tff(25,plain,
% 10.31/6.87 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((~(app(Y, Z) = X)) | ![X1: $i] : (ssItem(X1) => (~(app(app(Y, cons(X1, nil)), Z) = W))))))) | neq(U, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W))))))))))),
% 10.31/6.87 inference(rewrite,[status(thm)],[])).
% 10.31/6.87 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) => ((~(app(Y, Z) = X)) | ![X1: $i] : (ssItem(X1) => (~(app(app(Y, cons(X1, nil)), Z) = W))))))) | neq(U, nil))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 10.31/6.87 tff(27,plain,
% 10.31/6.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.87 inference(modus_ponens,[status(thm)],[26, 25])).
% 10.31/6.87 tff(28,plain,
% 10.31/6.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.87 inference(modus_ponens,[status(thm)],[27, 24])).
% 10.31/6.87 tff(29,plain,
% 10.31/6.87 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.87 inference(modus_ponens,[status(thm)],[28, 24])).
% 10.31/6.88 tff(30,plain,
% 10.31/6.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[29, 24])).
% 10.31/6.88 tff(31,plain,
% 10.31/6.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[30, 24])).
% 10.31/6.88 tff(32,plain,
% 10.31/6.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[31, 24])).
% 10.31/6.88 tff(33,plain,
% 10.31/6.88 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = X)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = W)))))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[32, 24])).
% 10.31/6.88 tff(34,plain,
% 10.31/6.88 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & (app(Y!51, Z!52) = X!50) & ssList(Z!52) & (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[33, 23])).
% 10.31/6.88 tff(35,plain,
% 10.31/6.88 (~((~ssItem(X1!53)) | (~(app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49)))),
% 10.31/6.88 inference(and_elim,[status(thm)],[34])).
% 10.31/6.88 tff(36,plain,
% 10.31/6.88 (app(app(Y!51, cons(X1!53, nil)), Z!52) = W!49),
% 10.31/6.88 inference(or_elim,[status(thm)],[35])).
% 10.31/6.88 tff(37,plain,
% 10.31/6.88 (W!49 = app(app(Y!51, cons(X1!53, nil)), Z!52)),
% 10.31/6.88 inference(symmetry,[status(thm)],[36])).
% 10.31/6.88 tff(38,plain,
% 10.31/6.88 (ssList(W!49)),
% 10.31/6.88 inference(and_elim,[status(thm)],[34])).
% 10.31/6.88 tff(39,plain,
% 10.31/6.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(40,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[39])).
% 10.31/6.88 tff(41,plain,
% 10.31/6.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(42,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[41])).
% 10.31/6.88 tff(43,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(transitivity,[status(thm)],[42, 40])).
% 10.31/6.88 tff(44,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(45,plain,
% 10.31/6.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(46,plain,
% 10.31/6.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[45])).
% 10.31/6.88 tff(47,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 10.31/6.88 tff(48,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[47, 46])).
% 10.31/6.88 tff(49,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[48, 44])).
% 10.31/6.88 tff(50,plain,(
% 10.31/6.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(skolemize,[status(sab)],[49])).
% 10.31/6.88 tff(51,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[50, 43])).
% 10.31/6.88 tff(52,plain,
% 10.31/6.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(53,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(54,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[53, 52])).
% 10.31/6.88 tff(55,plain,
% 10.31/6.88 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[54, 51, 38])).
% 10.31/6.88 tff(56,plain,
% 10.31/6.88 (ssList(nil) <=> ssList(nil)),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(57,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 10.31/6.88 tff(58,plain,
% 10.31/6.88 (ssList(nil)),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[57, 56])).
% 10.31/6.88 tff(59,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(60,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(61,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[60, 59])).
% 10.31/6.88 tff(62,plain,
% 10.31/6.88 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[61, 58, 55])).
% 10.31/6.88 tff(63,plain,
% 10.31/6.88 (U!47 = W!49),
% 10.31/6.88 inference(and_elim,[status(thm)],[34])).
% 10.31/6.88 tff(64,plain,
% 10.31/6.88 (W!49 = U!47),
% 10.31/6.88 inference(symmetry,[status(thm)],[63])).
% 10.31/6.88 tff(65,plain,
% 10.31/6.88 (neq(W!49, nil) <=> neq(U!47, nil)),
% 10.31/6.88 inference(monotonicity,[status(thm)],[64])).
% 10.31/6.88 tff(66,plain,
% 10.31/6.88 (neq(U!47, nil) <=> neq(W!49, nil)),
% 10.31/6.88 inference(symmetry,[status(thm)],[65])).
% 10.31/6.88 tff(67,plain,
% 10.31/6.88 ((~neq(U!47, nil)) <=> (~neq(W!49, nil))),
% 10.31/6.88 inference(monotonicity,[status(thm)],[66])).
% 10.31/6.88 tff(68,plain,
% 10.31/6.88 (~neq(U!47, nil)),
% 10.31/6.88 inference(and_elim,[status(thm)],[34])).
% 10.31/6.88 tff(69,plain,
% 10.31/6.88 (~neq(W!49, nil)),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[68, 67])).
% 10.31/6.88 tff(70,plain,
% 10.31/6.88 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 10.31/6.88 inference(tautology,[status(thm)],[])).
% 10.31/6.88 tff(71,plain,
% 10.31/6.88 (W!49 = nil),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[70, 69, 62])).
% 10.31/6.88 tff(72,plain,
% 10.31/6.88 (nil = W!49),
% 10.31/6.88 inference(symmetry,[status(thm)],[71])).
% 10.31/6.88 tff(73,plain,
% 10.31/6.88 (nil = app(app(Y!51, cons(X1!53, nil)), Z!52)),
% 10.31/6.88 inference(transitivity,[status(thm)],[72, 37])).
% 10.31/6.88 tff(74,plain,
% 10.31/6.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(75,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[74])).
% 10.31/6.88 tff(76,plain,
% 10.31/6.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(77,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[76])).
% 10.31/6.88 tff(78,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(transitivity,[status(thm)],[77, 75])).
% 10.31/6.88 tff(79,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(80,plain,
% 10.31/6.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(81,plain,
% 10.31/6.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[80])).
% 10.31/6.88 tff(82,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax16')).
% 10.31/6.88 tff(83,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[82, 81])).
% 10.31/6.88 tff(84,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[83, 79])).
% 10.31/6.88 tff(85,plain,(
% 10.31/6.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(skolemize,[status(sab)],[84])).
% 10.31/6.88 tff(86,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[85, 78])).
% 10.31/6.88 tff(87,plain,
% 10.31/6.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(88,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(89,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[88, 87])).
% 10.31/6.88 tff(90,plain,
% 10.31/6.88 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[89, 86, 58])).
% 10.31/6.88 tff(91,plain,
% 10.31/6.88 (ssItem(X1!53)),
% 10.31/6.88 inference(or_elim,[status(thm)],[35])).
% 10.31/6.88 tff(92,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X1!53)) | ssList(cons(X1!53, nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X1!53)) | ssList(cons(X1!53, nil)))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(93,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X1!53)) | ssList(cons(X1!53, nil)))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(94,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X1!53)) | ssList(cons(X1!53, nil))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[93, 92])).
% 10.31/6.88 tff(95,plain,
% 10.31/6.88 (ssList(cons(X1!53, nil))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[94, 91, 90])).
% 10.31/6.88 tff(96,plain,
% 10.31/6.88 (ssList(Y!51)),
% 10.31/6.88 inference(and_elim,[status(thm)],[34])).
% 10.31/6.88 tff(97,plain,
% 10.31/6.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(98,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[97])).
% 10.31/6.88 tff(99,plain,
% 10.31/6.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(100,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[99])).
% 10.31/6.88 tff(101,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 10.31/6.88 inference(transitivity,[status(thm)],[100, 98])).
% 10.31/6.88 tff(102,plain,
% 10.31/6.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(103,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[102])).
% 10.31/6.88 tff(104,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(105,plain,
% 10.31/6.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(106,plain,
% 10.31/6.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[105])).
% 10.31/6.88 tff(107,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax83')).
% 10.31/6.88 tff(108,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[107, 106])).
% 10.31/6.88 tff(109,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[108, 104])).
% 10.31/6.88 tff(110,plain,(
% 10.31/6.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 10.31/6.88 inference(skolemize,[status(sab)],[109])).
% 10.31/6.88 tff(111,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[110, 103])).
% 10.31/6.88 tff(112,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[111, 101])).
% 10.31/6.88 tff(113,plain,
% 10.31/6.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51)))))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(114,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51)))))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(115,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[114, 113])).
% 10.31/6.88 tff(116,plain,
% 10.31/6.88 (![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[115, 112, 96])).
% 10.31/6.88 tff(117,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | ((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | (~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(118,plain,
% 10.31/6.88 (((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = cons(X1!53, nil))) | (~(nil = Y!51)))))) <=> ((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(119,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | ((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = cons(X1!53, nil))) | (~(nil = Y!51))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | ((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil))))))))),
% 10.31/6.88 inference(monotonicity,[status(thm)],[118])).
% 10.31/6.88 tff(120,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | ((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = cons(X1!53, nil))) | (~(nil = Y!51))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | (~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))))))),
% 10.31/6.88 inference(transitivity,[status(thm)],[119, 117])).
% 10.31/6.88 tff(121,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | ((~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = cons(X1!53, nil))) | (~(nil = Y!51))))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(122,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssList(V)) | ((nil = app(Y!51, V)) <=> (~((~(nil = V)) | (~(nil = Y!51))))))) | (~ssList(cons(X1!53, nil))) | ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil))))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[121, 120])).
% 10.31/6.88 tff(123,plain,
% 10.31/6.88 ((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[122, 116, 95])).
% 10.31/6.88 tff(124,plain,
% 10.31/6.88 ((nil = cons(X1!53, nil)) <=> (cons(X1!53, nil) = nil)),
% 10.31/6.88 inference(commutativity,[status(thm)],[])).
% 10.31/6.88 tff(125,plain,
% 10.31/6.88 ((cons(X1!53, nil) = nil) <=> (nil = cons(X1!53, nil))),
% 10.31/6.88 inference(symmetry,[status(thm)],[124])).
% 10.31/6.88 tff(126,plain,
% 10.31/6.88 ((~(cons(X1!53, nil) = nil)) <=> (~(nil = cons(X1!53, nil)))),
% 10.31/6.88 inference(monotonicity,[status(thm)],[125])).
% 10.31/6.88 tff(127,plain,
% 10.31/6.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(128,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[127])).
% 10.31/6.88 tff(129,plain,
% 10.31/6.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(130,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[129])).
% 10.31/6.88 tff(131,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(transitivity,[status(thm)],[130, 128])).
% 10.31/6.88 tff(132,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(133,plain,
% 10.31/6.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(134,plain,
% 10.31/6.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[133])).
% 10.31/6.88 tff(135,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax18')).
% 10.31/6.88 tff(136,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[135, 134])).
% 10.31/6.88 tff(137,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[136, 132])).
% 10.31/6.88 tff(138,plain,(
% 10.31/6.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(skolemize,[status(sab)],[137])).
% 10.31/6.88 tff(139,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[138, 131])).
% 10.31/6.88 tff(140,plain,
% 10.31/6.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(141,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(142,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[141, 140])).
% 10.31/6.88 tff(143,plain,
% 10.31/6.88 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[142, 58, 139])).
% 10.31/6.88 tff(144,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(X1!53)) | (~(cons(X1!53, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(X1!53)) | (~(cons(X1!53, nil) = nil)))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(145,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(X1!53)) | (~(cons(X1!53, nil) = nil)))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(146,plain,
% 10.31/6.88 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(X1!53)) | (~(cons(X1!53, nil) = nil))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[145, 144])).
% 10.31/6.88 tff(147,plain,
% 10.31/6.88 (~(cons(X1!53, nil) = nil)),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[146, 91, 143])).
% 10.31/6.88 tff(148,plain,
% 10.31/6.88 (~(nil = cons(X1!53, nil))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[147, 126])).
% 10.31/6.88 tff(149,plain,
% 10.31/6.88 (((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))) | (nil = cons(X1!53, nil))),
% 10.31/6.88 inference(tautology,[status(thm)],[])).
% 10.31/6.88 tff(150,plain,
% 10.31/6.88 ((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[149, 148])).
% 10.31/6.88 tff(151,plain,
% 10.31/6.88 ((~((nil = app(Y!51, cons(X1!53, nil))) <=> (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil))))))) | (~(nil = app(Y!51, cons(X1!53, nil)))) | (~((~(nil = Y!51)) | (~(nil = cons(X1!53, nil)))))),
% 10.31/6.88 inference(tautology,[status(thm)],[])).
% 10.31/6.88 tff(152,plain,
% 10.31/6.88 (~(nil = app(Y!51, cons(X1!53, nil)))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[151, 150, 123])).
% 10.31/6.88 tff(153,plain,
% 10.31/6.88 (((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil))))) | (nil = app(Y!51, cons(X1!53, nil)))),
% 10.31/6.88 inference(tautology,[status(thm)],[])).
% 10.31/6.88 tff(154,plain,
% 10.31/6.88 ((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil))))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[153, 152])).
% 10.31/6.88 tff(155,plain,
% 10.31/6.88 ((~((nil = app(app(Y!51, cons(X1!53, nil)), Z!52)) <=> (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil)))))))) | (~(nil = app(app(Y!51, cons(X1!53, nil)), Z!52))) | (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil))))))),
% 10.31/6.88 inference(tautology,[status(thm)],[])).
% 10.31/6.88 tff(156,plain,
% 10.31/6.88 (~((nil = app(app(Y!51, cons(X1!53, nil)), Z!52)) <=> (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil)))))))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[155, 154, 73])).
% 10.31/6.88 tff(157,plain,
% 10.31/6.88 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(158,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[157])).
% 10.31/6.88 tff(159,plain,
% 10.31/6.88 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(160,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[159])).
% 10.31/6.88 tff(161,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(transitivity,[status(thm)],[160, 158])).
% 10.31/6.88 tff(162,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(163,plain,
% 10.31/6.88 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ssList(app(U, V))) <=> ((~ssList(V)) | ssList(app(U, V))))), (![V: $i] : (ssList(V) => ssList(app(U, V))) <=> ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))))),
% 10.31/6.88 inference(bind,[status(th)],[])).
% 10.31/6.88 tff(164,plain,
% 10.31/6.88 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(quant_intro,[status(thm)],[163])).
% 10.31/6.88 tff(165,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax26')).
% 10.31/6.88 tff(166,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[165, 164])).
% 10.31/6.88 tff(167,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[166, 162])).
% 10.31/6.88 tff(168,plain,(
% 10.31/6.88 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(skolemize,[status(sab)],[167])).
% 10.31/6.88 tff(169,plain,
% 10.31/6.88 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[168, 161])).
% 10.31/6.88 tff(170,plain,
% 10.31/6.88 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V))))),
% 10.31/6.88 inference(rewrite,[status(thm)],[])).
% 10.31/6.88 tff(171,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V))))),
% 10.31/6.88 inference(quant_inst,[status(thm)],[])).
% 10.31/6.88 tff(172,plain,
% 10.31/6.88 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))),
% 10.31/6.88 inference(modus_ponens,[status(thm)],[171, 170])).
% 10.31/6.88 tff(173,plain,
% 10.31/6.88 (![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))),
% 10.31/6.88 inference(unit_resolution,[status(thm)],[172, 169, 96])).
% 10.31/6.88 tff(174,plain,
% 10.31/6.88 (((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | ((~ssList(cons(X1!53, nil))) | ssList(app(Y!51, cons(X1!53, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | (~ssList(cons(X1!53, nil))) | ssList(app(Y!51, cons(X1!53, nil))))),
% 10.31/6.90 inference(rewrite,[status(thm)],[])).
% 10.31/6.90 tff(175,plain,
% 10.31/6.90 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | ((~ssList(cons(X1!53, nil))) | ssList(app(Y!51, cons(X1!53, nil))))),
% 10.31/6.90 inference(quant_inst,[status(thm)],[])).
% 10.31/6.90 tff(176,plain,
% 10.31/6.90 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!51, V)))) | (~ssList(cons(X1!53, nil))) | ssList(app(Y!51, cons(X1!53, nil)))),
% 10.31/6.90 inference(modus_ponens,[status(thm)],[175, 174])).
% 10.31/6.90 tff(177,plain,
% 10.31/6.90 (ssList(app(Y!51, cons(X1!53, nil)))),
% 10.31/6.90 inference(unit_resolution,[status(thm)],[176, 173, 95])).
% 10.31/6.90 tff(178,plain,
% 10.31/6.90 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(app(Y!51, cons(X1!53, nil)))) | ![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(app(Y!51, cons(X1!53, nil)))) | ![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil)))))))))),
% 10.31/6.90 inference(rewrite,[status(thm)],[])).
% 10.31/6.90 tff(179,plain,
% 10.31/6.90 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(app(Y!51, cons(X1!53, nil)))) | ![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil)))))))))),
% 10.31/6.90 inference(quant_inst,[status(thm)],[])).
% 10.31/6.90 tff(180,plain,
% 10.31/6.90 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(app(Y!51, cons(X1!53, nil)))) | ![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))),
% 10.31/6.90 inference(modus_ponens,[status(thm)],[179, 178])).
% 10.31/6.90 tff(181,plain,
% 10.31/6.90 (![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))),
% 10.31/6.90 inference(unit_resolution,[status(thm)],[180, 112, 177])).
% 10.31/6.90 tff(182,plain,
% 10.31/6.90 (ssList(Z!52)),
% 10.31/6.90 inference(and_elim,[status(thm)],[34])).
% 10.31/6.90 tff(183,plain,
% 10.31/6.90 (((~![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))) | ((~ssList(Z!52)) | ((nil = app(app(Y!51, cons(X1!53, nil)), Z!52)) <=> (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))) | (~ssList(Z!52)) | ((nil = app(app(Y!51, cons(X1!53, nil)), Z!52)) <=> (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))),
% 10.31/6.90 inference(rewrite,[status(thm)],[])).
% 10.31/6.90 tff(184,plain,
% 10.31/6.90 ((~![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))) | ((~ssList(Z!52)) | ((nil = app(app(Y!51, cons(X1!53, nil)), Z!52)) <=> (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))),
% 10.31/6.90 inference(quant_inst,[status(thm)],[])).
% 10.31/6.90 tff(185,plain,
% 10.31/6.90 ((~![V: $i] : ((~ssList(V)) | ((nil = app(app(Y!51, cons(X1!53, nil)), V)) <=> (~((~(nil = V)) | (~(nil = app(Y!51, cons(X1!53, nil))))))))) | (~ssList(Z!52)) | ((nil = app(app(Y!51, cons(X1!53, nil)), Z!52)) <=> (~((~(nil = Z!52)) | (~(nil = app(Y!51, cons(X1!53, nil)))))))),
% 10.31/6.90 inference(modus_ponens,[status(thm)],[184, 183])).
% 10.31/6.90 tff(186,plain,
% 10.31/6.90 ($false),
% 10.31/6.90 inference(unit_resolution,[status(thm)],[185, 182, 181, 156])).
% 10.31/6.90 % SZS output end Proof
%------------------------------------------------------------------------------