TSTP Solution File: SWC039+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC039+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 11:54:49 EDT 2022
% Result : Theorem 3.35s 2.40s
% Output : Proof 3.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC039+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.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 20:50:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 3.35/2.40 % SZS status Theorem
% 3.35/2.40 % SZS output start Proof
% 3.35/2.40 tff(app_type, type, (
% 3.35/2.40 app: ( $i * $i ) > $i)).
% 3.35/2.40 tff(tptp_fun_X1_53_type, type, (
% 3.35/2.40 tptp_fun_X1_53: $i)).
% 3.35/2.40 tff(tptp_fun_W_49_type, type, (
% 3.35/2.40 tptp_fun_W_49: $i)).
% 3.35/2.40 tff(tptp_fun_Z_52_type, type, (
% 3.35/2.40 tptp_fun_Z_52: $i)).
% 3.35/2.40 tff(nil_type, type, (
% 3.35/2.40 nil: $i)).
% 3.35/2.40 tff(ssList_type, type, (
% 3.35/2.40 ssList: $i > $o)).
% 3.35/2.40 tff(lt_type, type, (
% 3.35/2.40 lt: ( $i * $i ) > $o)).
% 3.35/2.40 tff(tptp_fun_Y_51_type, type, (
% 3.35/2.40 tptp_fun_Y_51: $i)).
% 3.35/2.40 tff(memberP_type, type, (
% 3.35/2.40 memberP: ( $i * $i ) > $o)).
% 3.35/2.40 tff(ssItem_type, type, (
% 3.35/2.40 ssItem: $i > $o)).
% 3.35/2.40 tff(tptp_fun_X_50_type, type, (
% 3.35/2.40 tptp_fun_X_50: $i)).
% 3.35/2.40 tff(cons_type, type, (
% 3.35/2.40 cons: ( $i * $i ) > $i)).
% 3.35/2.40 tff(tptp_fun_U_47_type, type, (
% 3.35/2.40 tptp_fun_U_47: $i)).
% 3.35/2.40 tff(tptp_fun_V_48_type, type, (
% 3.35/2.40 tptp_fun_V_48: $i)).
% 3.35/2.40 tff(1,plain,
% 3.35/2.40 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.35/2.40 inference(rewrite,[status(thm)],[])).
% 3.35/2.40 tff(2,plain,
% 3.35/2.40 ((ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.35/2.40 inference(rewrite,[status(thm)],[])).
% 3.35/2.40 tff(3,plain,
% 3.35/2.40 ((ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.35/2.40 inference(rewrite,[status(thm)],[])).
% 3.35/2.40 tff(4,plain,
% 3.35/2.40 (((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49)))))) <=> ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(5,plain,
% 3.38/2.40 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(6,plain,
% 3.38/2.40 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 3.38/2.40 inference(monotonicity,[status(thm)],[5, 4])).
% 3.38/2.40 tff(7,plain,
% 3.38/2.40 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.38/2.40 inference(transitivity,[status(thm)],[6, 3])).
% 3.38/2.40 tff(8,plain,
% 3.38/2.40 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(9,plain,
% 3.38/2.40 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 3.38/2.40 inference(monotonicity,[status(thm)],[8, 7])).
% 3.38/2.40 tff(10,plain,
% 3.38/2.40 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.38/2.40 inference(transitivity,[status(thm)],[9, 2])).
% 3.38/2.40 tff(11,plain,
% 3.38/2.40 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(12,plain,
% 3.38/2.40 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 3.38/2.40 inference(monotonicity,[status(thm)],[11, 10])).
% 3.38/2.40 tff(13,plain,
% 3.38/2.40 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & (((~(~ssItem(Y!51))) & ((~(~ssList(Z!52))) & ((~(~(app(app(Z!52, W!49), X1!53) = X!50))) & (~(~(cons(Y!51, nil) = W!49))) & (~(~ssList(X1!53))) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 3.38/2.40 inference(transitivity,[status(thm)],[12, 1])).
% 3.38/2.40 tff(14,plain,
% 3.38/2.40 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(15,plain,
% 3.38/2.40 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | (![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ![X1: $i] : (ssList(X1) => ((((~(cons(Y, nil) = W)) | (~(app(app(Z, W), X1) = X))) | ?[X2: $i] : ((ssItem(X2) & memberP(Z, X2)) & lt(Y, X2))) | ?[X3: $i] : ((ssItem(X3) & memberP(X1, X3)) & lt(X3, Y)))))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | (![Y: $i] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ![X1: $i] : (ssList(X1) => ((((~(cons(Y, nil) = W)) | (~(app(app(Z, W), X1) = X))) | ?[X2: $i] : ((ssItem(X2) & memberP(Z, X2)) & lt(Y, X2))) | ?[X3: $i] : ((ssItem(X3) & memberP(X1, X3)) & lt(X3, Y)))))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 3.38/2.40 tff(17,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.38/2.40 tff(18,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[17, 14])).
% 3.38/2.40 tff(19,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.38/2.40 tff(20,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[19, 14])).
% 3.38/2.40 tff(21,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[20, 14])).
% 3.38/2.40 tff(22,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.38/2.40 tff(23,plain,
% 3.38/2.40 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~(app(app(Z, W), X1) = X)) | (~(cons(Y, nil) = W)) | (~ssList(X1)) | ?[X2: $i] : (ssItem(X2) & memberP(Z, X2) & lt(Y, X2)) | ?[X3: $i] : (ssItem(X3) & memberP(X1, X3) & lt(X3, Y))))) & ((~(nil = X)) | (~(nil = W))))))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[22, 14])).
% 3.38/2.40 tff(24,plain,
% 3.38/2.40 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[23, 13])).
% 3.38/2.40 tff(25,plain,
% 3.38/2.40 (U!47 = W!49),
% 3.38/2.40 inference(and_elim,[status(thm)],[24])).
% 3.38/2.40 tff(26,plain,
% 3.38/2.40 ((nil = U!47) <=> (nil = W!49)),
% 3.38/2.40 inference(monotonicity,[status(thm)],[25])).
% 3.38/2.40 tff(27,plain,
% 3.38/2.40 ((~(nil = U!47)) <=> (~(nil = W!49))),
% 3.38/2.40 inference(monotonicity,[status(thm)],[26])).
% 3.38/2.40 tff(28,plain,
% 3.38/2.40 (~(nil = U!47)),
% 3.38/2.40 inference(and_elim,[status(thm)],[24])).
% 3.38/2.40 tff(29,plain,
% 3.38/2.40 (~(nil = W!49)),
% 3.38/2.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.38/2.40 tff(30,plain,
% 3.38/2.40 (((~(nil = W!49)) | (~(nil = X!50))) | (nil = W!49)),
% 3.38/2.40 inference(tautology,[status(thm)],[])).
% 3.38/2.40 tff(31,plain,
% 3.38/2.40 ((~(nil = W!49)) | (~(nil = X!50))),
% 3.38/2.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 3.38/2.40 tff(32,plain,
% 3.38/2.40 (((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))))),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(33,plain,
% 3.38/2.40 (((~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))) | (~((~(nil = W!49)) | (~(nil = X!50))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))))),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(34,plain,
% 3.38/2.40 ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2))) & ![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))) <=> (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))))),
% 3.38/2.40 inference(rewrite,[status(thm)],[])).
% 3.38/2.40 tff(35,plain,
% 3.38/2.40 (^[X3: $i] : trans(monotonicity(rewrite((ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)) <=> (~((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))), ((~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51))) <=> (~(~((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))))), rewrite((~(~((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))) <=> ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))), ((~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51))) <=> ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))),
% 3.38/2.40 inference(bind,[status(th)],[])).
% 3.38/2.40 tff(36,plain,
% 3.38/2.40 (![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51))) <=> ![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))),
% 3.38/2.40 inference(quant_intro,[status(thm)],[35])).
% 3.38/2.40 tff(37,plain,
% 3.38/2.40 (^[X2: $i] : trans(monotonicity(rewrite((ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2)) <=> (~((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2))))), ((~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) <=> (~(~((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2))))))), rewrite((~(~((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2))))) <=> ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))), ((~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) <=> ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(38,plain,
% 3.38/2.41 (![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) <=> ![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[37])).
% 3.38/2.41 tff(39,plain,
% 3.38/2.41 ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) <=> (ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2))) & ![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))),
% 3.38/2.41 inference(monotonicity,[status(thm)],[38, 36])).
% 3.38/2.41 tff(40,plain,
% 3.38/2.41 ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) <=> (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))))),
% 3.38/2.41 inference(transitivity,[status(thm)],[39, 34])).
% 3.38/2.41 tff(41,plain,
% 3.38/2.41 (((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))) <=> ((~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 3.38/2.41 inference(monotonicity,[status(thm)],[40])).
% 3.38/2.41 tff(42,plain,
% 3.38/2.41 (((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))))),
% 3.38/2.41 inference(transitivity,[status(thm)],[41, 33])).
% 3.38/2.41 tff(43,plain,
% 3.38/2.41 ((ssItem(Y!51) & ssList(Z!52) & (app(app(Z!52, W!49), X1!53) = X!50) & (cons(Y!51, nil) = W!49) & ssList(X1!53) & ![X2: $i] : (~(ssItem(X2) & memberP(Z!52, X2) & lt(Y!51, X2))) & ![X3: $i] : (~(ssItem(X3) & memberP(X1!53, X3) & lt(X3, Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))),
% 3.38/2.41 inference(and_elim,[status(thm)],[24])).
% 3.38/2.41 tff(44,plain,
% 3.38/2.41 ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 3.38/2.41 tff(45,plain,
% 3.38/2.41 ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[44, 32])).
% 3.38/2.41 tff(46,plain,
% 3.38/2.41 (~((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51)))))),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[45, 31])).
% 3.38/2.41 tff(47,plain,
% 3.38/2.41 (((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))) | ssList(Z!52)),
% 3.38/2.41 inference(tautology,[status(thm)],[])).
% 3.38/2.41 tff(48,plain,
% 3.38/2.41 (ssList(Z!52)),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 3.38/2.41 tff(49,plain,
% 3.38/2.41 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(50,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[49])).
% 3.38/2.41 tff(51,plain,
% 3.38/2.41 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(52,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[51])).
% 3.38/2.41 tff(53,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(transitivity,[status(thm)],[52, 50])).
% 3.38/2.41 tff(54,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(55,plain,
% 3.38/2.41 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), (![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(56,plain,
% 3.38/2.41 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[55])).
% 3.38/2.41 tff(57,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax82')).
% 3.38/2.41 tff(58,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.38/2.41 tff(59,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 3.38/2.41 tff(60,plain,(
% 3.38/2.41 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(skolemize,[status(sab)],[59])).
% 3.38/2.41 tff(61,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[60, 53])).
% 3.38/2.41 tff(62,plain,
% 3.38/2.41 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W))))))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(63,plain,
% 3.38/2.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W))))))),
% 3.38/2.41 inference(quant_inst,[status(thm)],[])).
% 3.38/2.41 tff(64,plain,
% 3.38/2.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W)))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 3.38/2.41 tff(65,plain,
% 3.38/2.41 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W)))))),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[64, 61, 48])).
% 3.38/2.41 tff(66,plain,
% 3.38/2.41 (ssList(W!49)),
% 3.38/2.41 inference(and_elim,[status(thm)],[24])).
% 3.38/2.41 tff(67,plain,
% 3.38/2.41 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W)))))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(68,plain,
% 3.38/2.41 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W)))))),
% 3.38/2.41 inference(quant_inst,[status(thm)],[])).
% 3.38/2.41 tff(69,plain,
% 3.38/2.41 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, V), W) = app(Z!52, app(V, W)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.38/2.41 tff(70,plain,
% 3.38/2.41 (![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W))))),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[69, 66, 65])).
% 3.38/2.41 tff(71,plain,
% 3.38/2.41 (((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))) | ssList(X1!53)),
% 3.38/2.41 inference(tautology,[status(thm)],[])).
% 3.38/2.41 tff(72,plain,
% 3.38/2.41 (ssList(X1!53)),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[71, 46])).
% 3.38/2.41 tff(73,plain,
% 3.38/2.41 (((~![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W))))) | ((~ssList(X1!53)) | (app(app(Z!52, W!49), X1!53) = app(Z!52, app(W!49, X1!53))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W))))) | (~ssList(X1!53)) | (app(app(Z!52, W!49), X1!53) = app(Z!52, app(W!49, X1!53))))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(74,plain,
% 3.38/2.41 ((~![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W))))) | ((~ssList(X1!53)) | (app(app(Z!52, W!49), X1!53) = app(Z!52, app(W!49, X1!53))))),
% 3.38/2.41 inference(quant_inst,[status(thm)],[])).
% 3.38/2.41 tff(75,plain,
% 3.38/2.41 ((~![W: $i] : ((~ssList(W)) | (app(app(Z!52, W!49), W) = app(Z!52, app(W!49, W))))) | (~ssList(X1!53)) | (app(app(Z!52, W!49), X1!53) = app(Z!52, app(W!49, X1!53)))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 3.38/2.41 tff(76,plain,
% 3.38/2.41 (app(app(Z!52, W!49), X1!53) = app(Z!52, app(W!49, X1!53))),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[75, 72, 70])).
% 3.38/2.41 tff(77,plain,
% 3.38/2.41 (((~ssItem(Y!51)) | (~(cons(Y!51, nil) = W!49)) | (~ssList(Z!52)) | (~(app(app(Z!52, W!49), X1!53) = X!50)) | (~ssList(X1!53)) | (~![X2: $i] : ((~ssItem(X2)) | (~memberP(Z!52, X2)) | (~lt(Y!51, X2)))) | (~![X3: $i] : ((~ssItem(X3)) | (~memberP(X1!53, X3)) | (~lt(X3, Y!51))))) | (app(app(Z!52, W!49), X1!53) = X!50)),
% 3.38/2.41 inference(tautology,[status(thm)],[])).
% 3.38/2.41 tff(78,plain,
% 3.38/2.41 (app(app(Z!52, W!49), X1!53) = X!50),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[77, 46])).
% 3.38/2.41 tff(79,plain,
% 3.38/2.41 (X!50 = app(app(Z!52, W!49), X1!53)),
% 3.38/2.41 inference(symmetry,[status(thm)],[78])).
% 3.38/2.41 tff(80,plain,
% 3.38/2.41 (V!48 = X!50),
% 3.38/2.41 inference(and_elim,[status(thm)],[24])).
% 3.38/2.41 tff(81,plain,
% 3.38/2.41 (nil = V!48),
% 3.38/2.41 inference(and_elim,[status(thm)],[24])).
% 3.38/2.41 tff(82,plain,
% 3.38/2.41 (nil = app(Z!52, app(W!49, X1!53))),
% 3.38/2.41 inference(transitivity,[status(thm)],[81, 80, 79, 76])).
% 3.38/2.41 tff(83,plain,
% 3.38/2.41 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(84,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[83])).
% 3.38/2.41 tff(85,plain,
% 3.38/2.41 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(86,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[85])).
% 3.38/2.41 tff(87,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(transitivity,[status(thm)],[86, 84])).
% 3.38/2.41 tff(88,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(89,plain,
% 3.38/2.41 (^[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))))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(90,plain,
% 3.38/2.41 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[89])).
% 3.38/2.41 tff(91,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax26')).
% 3.38/2.41 tff(92,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 3.38/2.41 tff(93,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[92, 88])).
% 3.38/2.41 tff(94,plain,(
% 3.38/2.41 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(skolemize,[status(sab)],[93])).
% 3.38/2.41 tff(95,plain,
% 3.38/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[94, 87])).
% 3.38/2.41 tff(96,plain,
% 3.38/2.41 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ssList(app(W!49, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ssList(app(W!49, V))))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(97,plain,
% 3.38/2.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ssList(app(W!49, V))))),
% 3.38/2.41 inference(quant_inst,[status(thm)],[])).
% 3.38/2.41 tff(98,plain,
% 3.38/2.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ssList(app(W!49, V)))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 3.38/2.41 tff(99,plain,
% 3.38/2.41 (![V: $i] : ((~ssList(V)) | ssList(app(W!49, V)))),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[98, 95, 66])).
% 3.38/2.41 tff(100,plain,
% 3.38/2.41 (((~![V: $i] : ((~ssList(V)) | ssList(app(W!49, V)))) | ((~ssList(X1!53)) | ssList(app(W!49, X1!53)))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(W!49, V)))) | (~ssList(X1!53)) | ssList(app(W!49, X1!53)))),
% 3.38/2.41 inference(rewrite,[status(thm)],[])).
% 3.38/2.41 tff(101,plain,
% 3.38/2.41 ((~![V: $i] : ((~ssList(V)) | ssList(app(W!49, V)))) | ((~ssList(X1!53)) | ssList(app(W!49, X1!53)))),
% 3.38/2.41 inference(quant_inst,[status(thm)],[])).
% 3.38/2.41 tff(102,plain,
% 3.38/2.41 ((~![V: $i] : ((~ssList(V)) | ssList(app(W!49, V)))) | (~ssList(X1!53)) | ssList(app(W!49, X1!53))),
% 3.38/2.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 3.38/2.41 tff(103,plain,
% 3.38/2.41 (ssList(app(W!49, X1!53))),
% 3.38/2.41 inference(unit_resolution,[status(thm)],[102, 72, 99])).
% 3.38/2.41 tff(104,plain,
% 3.38/2.41 (^[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))))))))),
% 3.38/2.41 inference(bind,[status(th)],[])).
% 3.38/2.41 tff(105,plain,
% 3.38/2.41 (![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)))))))),
% 3.38/2.41 inference(quant_intro,[status(thm)],[104])).
% 3.38/2.41 tff(106,plain,
% 3.38/2.41 (^[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))))))))),
% 3.39/2.41 inference(bind,[status(th)],[])).
% 3.39/2.41 tff(107,plain,
% 3.39/2.41 (![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)))))))),
% 3.39/2.41 inference(quant_intro,[status(thm)],[106])).
% 3.39/2.41 tff(108,plain,
% 3.39/2.41 (![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)))))))),
% 3.39/2.41 inference(transitivity,[status(thm)],[107, 105])).
% 3.39/2.41 tff(109,plain,
% 3.39/2.41 (^[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))))))))),
% 3.39/2.41 inference(bind,[status(th)],[])).
% 3.39/2.41 tff(110,plain,
% 3.39/2.41 (![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)))))))),
% 3.39/2.41 inference(quant_intro,[status(thm)],[109])).
% 3.39/2.41 tff(111,plain,
% 3.39/2.41 (![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)))))),
% 3.39/2.41 inference(rewrite,[status(thm)],[])).
% 3.39/2.41 tff(112,plain,
% 3.39/2.41 (^[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)))))))),
% 3.39/2.41 inference(bind,[status(th)],[])).
% 3.39/2.41 tff(113,plain,
% 3.39/2.41 (![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)))))),
% 3.39/2.41 inference(quant_intro,[status(thm)],[112])).
% 3.39/2.41 tff(114,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 3.39/2.41 tff(115,plain,
% 3.39/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 3.39/2.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 3.39/2.41 tff(116,plain,
% 3.39/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 3.39/2.41 inference(modus_ponens,[status(thm)],[115, 111])).
% 3.39/2.41 tff(117,plain,(
% 3.39/2.41 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 3.39/2.41 inference(skolemize,[status(sab)],[116])).
% 3.39/2.41 tff(118,plain,
% 3.39/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 3.39/2.41 inference(modus_ponens,[status(thm)],[117, 110])).
% 3.39/2.41 tff(119,plain,
% 3.39/2.41 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 3.39/2.41 inference(modus_ponens,[status(thm)],[118, 108])).
% 3.39/2.41 tff(120,plain,
% 3.39/2.41 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52)))))))),
% 3.39/2.41 inference(rewrite,[status(thm)],[])).
% 3.39/2.41 tff(121,plain,
% 3.39/2.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52)))))))),
% 3.39/2.41 inference(quant_inst,[status(thm)],[])).
% 3.39/2.41 tff(122,plain,
% 3.39/2.41 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(Z!52)) | ![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52))))))),
% 3.39/2.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 3.39/2.42 tff(123,plain,
% 3.39/2.42 (![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52))))))),
% 3.39/2.42 inference(unit_resolution,[status(thm)],[122, 119, 48])).
% 3.39/2.42 tff(124,plain,
% 3.39/2.42 (((~![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52))))))) | ((~ssList(app(W!49, X1!53))) | ((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52))))))) | (~ssList(app(W!49, X1!53))) | ((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))))))),
% 3.39/2.42 inference(rewrite,[status(thm)],[])).
% 3.39/2.42 tff(125,plain,
% 3.39/2.42 ((~![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52))))))) | ((~ssList(app(W!49, X1!53))) | ((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))))))),
% 3.39/2.42 inference(quant_inst,[status(thm)],[])).
% 3.39/2.42 tff(126,plain,
% 3.39/2.42 ((~![V: $i] : ((~ssList(V)) | ((nil = app(Z!52, V)) <=> (~((~(nil = V)) | (~(nil = Z!52))))))) | (~ssList(app(W!49, X1!53))) | ((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52)))))),
% 3.39/2.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.39/2.42 tff(127,plain,
% 3.39/2.42 ((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))))),
% 3.39/2.42 inference(unit_resolution,[status(thm)],[126, 123, 103])).
% 3.39/2.42 tff(128,plain,
% 3.39/2.42 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49)))))))),
% 3.39/2.42 inference(rewrite,[status(thm)],[])).
% 3.39/2.42 tff(129,plain,
% 3.39/2.42 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49)))))))),
% 3.39/2.42 inference(quant_inst,[status(thm)],[])).
% 3.39/2.42 tff(130,plain,
% 3.39/2.42 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))),
% 3.39/2.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 3.39/2.42 tff(131,plain,
% 3.39/2.42 (![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))),
% 3.39/2.42 inference(unit_resolution,[status(thm)],[130, 119, 66])).
% 3.39/2.42 tff(132,plain,
% 3.39/2.42 (((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | (~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53))))))),
% 3.39/2.43 inference(rewrite,[status(thm)],[])).
% 3.39/2.43 tff(133,plain,
% 3.39/2.43 (((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = X1!53)) | (~(nil = W!49)))))) <=> ((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53))))))),
% 3.39/2.43 inference(rewrite,[status(thm)],[])).
% 3.39/2.43 tff(134,plain,
% 3.39/2.43 (((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = X1!53)) | (~(nil = W!49))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53)))))))),
% 3.39/2.43 inference(monotonicity,[status(thm)],[133])).
% 3.39/2.43 tff(135,plain,
% 3.39/2.43 (((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = X1!53)) | (~(nil = W!49))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | (~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53))))))),
% 3.39/2.43 inference(transitivity,[status(thm)],[134, 132])).
% 3.39/2.43 tff(136,plain,
% 3.39/2.43 ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = X1!53)) | (~(nil = W!49))))))),
% 3.39/2.43 inference(quant_inst,[status(thm)],[])).
% 3.39/2.43 tff(137,plain,
% 3.39/2.43 ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | (~ssList(X1!53)) | ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53)))))),
% 3.39/2.43 inference(modus_ponens,[status(thm)],[136, 135])).
% 3.39/2.43 tff(138,plain,
% 3.39/2.43 ((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53))))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[137, 72, 131])).
% 3.39/2.43 tff(139,plain,
% 3.39/2.43 (((~(nil = W!49)) | (~(nil = X1!53))) | (nil = W!49)),
% 3.39/2.43 inference(tautology,[status(thm)],[])).
% 3.39/2.43 tff(140,plain,
% 3.39/2.43 ((~(nil = W!49)) | (~(nil = X1!53))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[139, 29])).
% 3.39/2.43 tff(141,plain,
% 3.39/2.43 ((~((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53)))))) | (~(nil = app(W!49, X1!53))) | (~((~(nil = W!49)) | (~(nil = X1!53))))),
% 3.39/2.43 inference(tautology,[status(thm)],[])).
% 3.39/2.43 tff(142,plain,
% 3.39/2.43 ((~((nil = app(W!49, X1!53)) <=> (~((~(nil = W!49)) | (~(nil = X1!53)))))) | (~(nil = app(W!49, X1!53)))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[141, 140])).
% 3.39/2.43 tff(143,plain,
% 3.39/2.43 (~(nil = app(W!49, X1!53))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[142, 138])).
% 3.39/2.43 tff(144,plain,
% 3.39/2.43 (((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))) | (nil = app(W!49, X1!53))),
% 3.39/2.43 inference(tautology,[status(thm)],[])).
% 3.39/2.43 tff(145,plain,
% 3.39/2.43 ((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[144, 143])).
% 3.39/2.43 tff(146,plain,
% 3.39/2.43 ((~((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52)))))) | (~(nil = app(Z!52, app(W!49, X1!53)))) | (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52))))),
% 3.39/2.43 inference(tautology,[status(thm)],[])).
% 3.39/2.43 tff(147,plain,
% 3.39/2.43 ((~((nil = app(Z!52, app(W!49, X1!53))) <=> (~((~(nil = app(W!49, X1!53))) | (~(nil = Z!52)))))) | (~(nil = app(Z!52, app(W!49, X1!53))))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[146, 145])).
% 3.39/2.43 tff(148,plain,
% 3.39/2.43 (~(nil = app(Z!52, app(W!49, X1!53)))),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[147, 127])).
% 3.39/2.43 tff(149,plain,
% 3.39/2.43 ($false),
% 3.39/2.43 inference(unit_resolution,[status(thm)],[148, 82])).
% 3.39/2.43 % SZS output end Proof
%------------------------------------------------------------------------------