TSTP Solution File: SWC213+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC213+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 11:56:11 EDT 2022
% Result : Theorem 1.50s 1.21s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC213+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 22:44:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.50/1.21 % SZS status Theorem
% 1.50/1.21 % SZS output start Proof
% 1.50/1.21 tff(app_type, type, (
% 1.50/1.21 app: ( $i * $i ) > $i)).
% 1.50/1.21 tff(tptp_fun_W_49_type, type, (
% 1.50/1.21 tptp_fun_W_49: $i)).
% 1.50/1.21 tff(nil_type, type, (
% 1.50/1.21 nil: $i)).
% 1.50/1.21 tff(ssList_type, type, (
% 1.50/1.21 ssList: $i > $o)).
% 1.50/1.21 tff(cons_type, type, (
% 1.50/1.21 cons: ( $i * $i ) > $i)).
% 1.50/1.21 tff(tptp_fun_Z_52_type, type, (
% 1.50/1.21 tptp_fun_Z_52: $i)).
% 1.50/1.21 tff(ssItem_type, type, (
% 1.50/1.21 ssItem: $i > $o)).
% 1.50/1.21 tff(tptp_fun_Y_51_type, type, (
% 1.50/1.21 tptp_fun_Y_51: $i)).
% 1.50/1.21 tff(equalelemsP_type, type, (
% 1.50/1.21 equalelemsP: $i > $o)).
% 1.50/1.21 tff(tptp_fun_X_50_type, type, (
% 1.50/1.21 tptp_fun_X_50: $i)).
% 1.50/1.21 tff(tptp_fun_V_48_type, type, (
% 1.50/1.21 tptp_fun_V_48: $i)).
% 1.50/1.21 tff(tptp_fun_U_47_type, type, (
% 1.50/1.21 tptp_fun_U_47: $i)).
% 1.50/1.21 tff(neq_type, type, (
% 1.50/1.21 neq: ( $i * $i ) > $o)).
% 1.50/1.21 tff(segmentP_type, type, (
% 1.50/1.21 segmentP: ( $i * $i ) > $o)).
% 1.50/1.21 tff(1,plain,
% 1.50/1.21 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(2,plain,
% 1.50/1.21 ((ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(3,plain,
% 1.50/1.21 ((ssList(W!49) & ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(4,plain,
% 1.50/1.22 (((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(5,plain,
% 1.50/1.22 ((ssList(Y!51) & ((app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> (ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(6,plain,
% 1.50/1.22 (((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))) <=> ((app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(7,plain,
% 1.50/1.22 ((~(~ssList(Y!51))) <=> ssList(Y!51)),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(8,plain,
% 1.50/1.22 (((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> (ssList(Y!51) & ((app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))),
% 1.53/1.22 inference(monotonicity,[status(thm)],[7, 6])).
% 1.53/1.22 tff(9,plain,
% 1.53/1.22 (((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))) <=> (ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.53/1.22 inference(transitivity,[status(thm)],[8, 5])).
% 1.53/1.22 tff(10,plain,
% 1.53/1.22 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 1.53/1.22 inference(rewrite,[status(thm)],[])).
% 1.53/1.22 tff(11,plain,
% 1.53/1.22 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 1.53/1.22 inference(rewrite,[status(thm)],[])).
% 1.53/1.22 tff(12,plain,
% 1.53/1.22 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 1.53/1.22 inference(rewrite,[status(thm)],[])).
% 1.53/1.22 tff(13,plain,
% 1.53/1.22 ((~(~neq(V!48, nil))) <=> neq(V!48, nil)),
% 1.53/1.22 inference(rewrite,[status(thm)],[])).
% 1.53/1.22 tff(14,plain,
% 1.53/1.22 (((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))) <=> ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & (ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))),
% 1.53/1.22 inference(monotonicity,[status(thm)],[13, 12, 11, 10, 9])).
% 1.53/1.22 tff(15,plain,
% 1.53/1.22 (((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))) <=> ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.53/1.22 inference(transitivity,[status(thm)],[14, 4])).
% 1.53/1.22 tff(16,plain,
% 1.53/1.22 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.53/1.22 inference(rewrite,[status(thm)],[])).
% 1.53/1.22 tff(17,plain,
% 1.53/1.22 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))))) <=> (ssList(W!49) & ((~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))),
% 1.53/1.22 inference(monotonicity,[status(thm)],[16, 15])).
% 1.53/1.22 tff(18,plain,
% 1.53/1.22 (((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))))) <=> (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.53/1.22 inference(transitivity,[status(thm)],[17, 3])).
% 1.53/1.22 tff(19,plain,
% 1.53/1.22 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.53/1.22 inference(rewrite,[status(thm)],[])).
% 1.53/1.22 tff(20,plain,
% 1.53/1.22 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))),
% 1.53/1.22 inference(monotonicity,[status(thm)],[19, 18])).
% 1.53/1.22 tff(21,plain,
% 1.53/1.22 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))))) <=> (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.53/1.23 inference(transitivity,[status(thm)],[20, 2])).
% 1.53/1.23 tff(22,plain,
% 1.53/1.23 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(23,plain,
% 1.53/1.23 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))))),
% 1.53/1.23 inference(monotonicity,[status(thm)],[22, 21])).
% 1.53/1.23 tff(24,plain,
% 1.53/1.23 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~neq(U!47, nil)) & (~(~neq(V!48, nil))) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49))))))),
% 1.53/1.23 inference(transitivity,[status(thm)],[23, 1])).
% 1.53/1.23 tff(25,plain,
% 1.53/1.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W)))))))))))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(26,plain,
% 1.53/1.23 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W))))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : ((ssList(X5) & (app(cons(X4, nil), X5) = Z)) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W)))))))) | neq(U, nil)) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W)))))))))))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(27,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W))))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : ((ssList(X5) & (app(cons(X4, nil), X5) = Z)) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W)))))))) | neq(U, nil)) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 1.53/1.23 tff(28,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.53/1.23 tff(29,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[28, 25])).
% 1.53/1.23 tff(30,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.53/1.23 tff(31,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[30, 25])).
% 1.53/1.23 tff(32,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[31, 25])).
% 1.53/1.23 tff(33,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.53/1.23 tff(34,plain,
% 1.53/1.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W))))))))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[33, 25])).
% 1.53/1.23 tff(35,plain,
% 1.53/1.23 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~neq(U!47, nil)) & neq(V!48, nil) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ssList(Y!51) & (app(app(Y!51, W!49), Z!52) = X!50) & equalelemsP(W!49) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = W!49))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!52)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = W!49)))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[34, 24])).
% 1.53/1.23 tff(36,plain,
% 1.53/1.23 (ssList(W!49)),
% 1.53/1.23 inference(and_elim,[status(thm)],[35])).
% 1.53/1.23 tff(37,plain,
% 1.53/1.23 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(38,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[37])).
% 1.53/1.23 tff(39,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(40,plain,
% 1.53/1.23 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(41,plain,
% 1.53/1.23 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[40])).
% 1.53/1.23 tff(42,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 1.53/1.23 tff(43,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.53/1.23 tff(44,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.53/1.23 tff(45,plain,(
% 1.53/1.23 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(skolemize,[status(sab)],[44])).
% 1.53/1.23 tff(46,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.53/1.23 tff(47,plain,
% 1.53/1.23 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(48,plain,
% 1.53/1.23 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 1.53/1.23 inference(quant_inst,[status(thm)],[])).
% 1.53/1.23 tff(49,plain,
% 1.53/1.23 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49)),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.53/1.23 tff(50,plain,
% 1.53/1.23 (app(nil, W!49) = W!49),
% 1.53/1.23 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 1.53/1.23 tff(51,plain,
% 1.53/1.23 ((nil = app(nil, W!49)) <=> (nil = W!49)),
% 1.53/1.23 inference(monotonicity,[status(thm)],[50])).
% 1.53/1.23 tff(52,plain,
% 1.53/1.23 ((nil = W!49) <=> (nil = app(nil, W!49))),
% 1.53/1.23 inference(symmetry,[status(thm)],[51])).
% 1.53/1.23 tff(53,plain,
% 1.53/1.23 ((W!49 = nil) <=> (nil = W!49)),
% 1.53/1.23 inference(commutativity,[status(thm)],[])).
% 1.53/1.23 tff(54,plain,
% 1.53/1.23 ((W!49 = nil) <=> (nil = app(nil, W!49))),
% 1.53/1.23 inference(transitivity,[status(thm)],[53, 52])).
% 1.53/1.23 tff(55,plain,
% 1.53/1.23 (^[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))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(56,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[55])).
% 1.53/1.23 tff(57,plain,
% 1.53/1.23 (^[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))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(58,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[57])).
% 1.53/1.23 tff(59,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(transitivity,[status(thm)],[58, 56])).
% 1.53/1.23 tff(60,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(61,plain,
% 1.53/1.23 (^[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)))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(62,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[61])).
% 1.53/1.23 tff(63,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 1.53/1.23 tff(64,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.53/1.23 tff(65,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.53/1.23 tff(66,plain,(
% 1.53/1.23 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.53/1.23 inference(skolemize,[status(sab)],[65])).
% 1.53/1.23 tff(67,plain,
% 1.53/1.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.53/1.23 tff(68,plain,
% 1.53/1.23 (((~![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)))))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(69,plain,
% 1.53/1.23 ((~![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)))))),
% 1.53/1.23 inference(quant_inst,[status(thm)],[])).
% 1.53/1.23 tff(70,plain,
% 1.53/1.23 ((~![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))))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.53/1.23 tff(71,plain,
% 1.53/1.23 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 1.53/1.23 inference(unit_resolution,[status(thm)],[70, 67, 36])).
% 1.53/1.23 tff(72,plain,
% 1.53/1.23 (ssList(nil) <=> ssList(nil)),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(73,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 1.53/1.23 tff(74,plain,
% 1.53/1.23 (ssList(nil)),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.53/1.23 tff(75,plain,
% 1.53/1.23 (((~![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))))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(76,plain,
% 1.53/1.23 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 1.53/1.23 inference(quant_inst,[status(thm)],[])).
% 1.53/1.23 tff(77,plain,
% 1.53/1.23 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.53/1.23 tff(78,plain,
% 1.53/1.23 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 1.53/1.23 inference(unit_resolution,[status(thm)],[77, 74, 71])).
% 1.53/1.23 tff(79,plain,
% 1.53/1.23 (U!47 = W!49),
% 1.53/1.23 inference(and_elim,[status(thm)],[35])).
% 1.53/1.23 tff(80,plain,
% 1.53/1.23 (W!49 = U!47),
% 1.53/1.23 inference(symmetry,[status(thm)],[79])).
% 1.53/1.23 tff(81,plain,
% 1.53/1.23 (neq(W!49, nil) <=> neq(U!47, nil)),
% 1.53/1.23 inference(monotonicity,[status(thm)],[80])).
% 1.53/1.23 tff(82,plain,
% 1.53/1.23 (neq(U!47, nil) <=> neq(W!49, nil)),
% 1.53/1.23 inference(symmetry,[status(thm)],[81])).
% 1.53/1.23 tff(83,plain,
% 1.53/1.23 ((~neq(U!47, nil)) <=> (~neq(W!49, nil))),
% 1.53/1.23 inference(monotonicity,[status(thm)],[82])).
% 1.53/1.23 tff(84,plain,
% 1.53/1.23 (~neq(U!47, nil)),
% 1.53/1.23 inference(and_elim,[status(thm)],[35])).
% 1.53/1.23 tff(85,plain,
% 1.53/1.23 (~neq(W!49, nil)),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.53/1.23 tff(86,plain,
% 1.53/1.23 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 1.53/1.23 inference(tautology,[status(thm)],[])).
% 1.53/1.23 tff(87,plain,
% 1.53/1.23 (W!49 = nil),
% 1.53/1.23 inference(unit_resolution,[status(thm)],[86, 85, 78])).
% 1.53/1.23 tff(88,plain,
% 1.53/1.23 (nil = app(nil, W!49)),
% 1.53/1.23 inference(modus_ponens,[status(thm)],[87, 54])).
% 1.53/1.23 tff(89,plain,
% 1.53/1.23 (^[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))))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(90,plain,
% 1.53/1.23 (![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)))))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[89])).
% 1.53/1.23 tff(91,plain,
% 1.53/1.23 (^[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))))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(92,plain,
% 1.53/1.23 (![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)))))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[91])).
% 1.53/1.23 tff(93,plain,
% 1.53/1.23 (![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)))))))),
% 1.53/1.23 inference(transitivity,[status(thm)],[92, 90])).
% 1.53/1.23 tff(94,plain,
% 1.53/1.23 (^[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))))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(95,plain,
% 1.53/1.23 (![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)))))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[94])).
% 1.53/1.23 tff(96,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(rewrite,[status(thm)],[])).
% 1.53/1.23 tff(97,plain,
% 1.53/1.23 (^[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)))))))),
% 1.53/1.23 inference(bind,[status(th)],[])).
% 1.53/1.23 tff(98,plain,
% 1.53/1.23 (![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)))))),
% 1.53/1.23 inference(quant_intro,[status(thm)],[97])).
% 1.53/1.23 tff(99,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')).
% 1.53/1.24 tff(100,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.53/1.24 tff(101,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.53/1.24 tff(102,plain,(
% 1.53/1.24 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 1.53/1.24 inference(skolemize,[status(sab)],[101])).
% 1.53/1.24 tff(103,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[102, 95])).
% 1.53/1.24 tff(104,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[103, 93])).
% 1.53/1.24 tff(105,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(106,plain,
% 1.53/1.24 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil))))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(107,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))))),
% 1.53/1.24 inference(monotonicity,[status(thm)],[106])).
% 1.53/1.24 tff(108,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 1.53/1.24 inference(transitivity,[status(thm)],[107, 105])).
% 1.53/1.24 tff(109,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(110,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.53/1.24 tff(111,plain,
% 1.53/1.24 (![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[110, 74, 104])).
% 1.53/1.24 tff(112,plain,
% 1.53/1.24 (((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | ((~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | (~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(113,plain,
% 1.53/1.24 ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | ((~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(114,plain,
% 1.53/1.24 ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | (~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.53/1.24 tff(115,plain,
% 1.53/1.24 ((nil = app(nil, W!49)) <=> (nil = W!49)),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[114, 36, 111])).
% 1.53/1.24 tff(116,plain,
% 1.53/1.24 (ssList(X!50)),
% 1.53/1.24 inference(and_elim,[status(thm)],[35])).
% 1.53/1.24 tff(117,plain,
% 1.53/1.24 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(118,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[117])).
% 1.53/1.24 tff(119,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(120,plain,
% 1.53/1.24 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(121,plain,
% 1.53/1.24 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[120])).
% 1.53/1.24 tff(122,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 1.53/1.24 tff(123,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.53/1.24 tff(124,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[123, 119])).
% 1.53/1.24 tff(125,plain,(
% 1.53/1.24 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(skolemize,[status(sab)],[124])).
% 1.53/1.24 tff(126,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.53/1.24 tff(127,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(128,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(129,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.53/1.24 tff(130,plain,
% 1.53/1.24 (segmentP(nil, X!50) <=> (nil = X!50)),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[129, 126, 116])).
% 1.53/1.24 tff(131,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(132,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(133,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.53/1.24 tff(134,plain,
% 1.53/1.24 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[133, 67, 116])).
% 1.53/1.24 tff(135,plain,
% 1.53/1.24 (((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(136,plain,
% 1.53/1.24 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(137,plain,
% 1.53/1.24 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.53/1.24 tff(138,plain,
% 1.53/1.24 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[137, 74, 134])).
% 1.53/1.24 tff(139,plain,
% 1.53/1.24 (V!48 = X!50),
% 1.53/1.24 inference(and_elim,[status(thm)],[35])).
% 1.53/1.24 tff(140,plain,
% 1.53/1.24 (X!50 = V!48),
% 1.53/1.24 inference(symmetry,[status(thm)],[139])).
% 1.53/1.24 tff(141,plain,
% 1.53/1.24 (neq(X!50, nil) <=> neq(V!48, nil)),
% 1.53/1.24 inference(monotonicity,[status(thm)],[140])).
% 1.53/1.24 tff(142,plain,
% 1.53/1.24 (neq(V!48, nil) <=> neq(X!50, nil)),
% 1.53/1.24 inference(symmetry,[status(thm)],[141])).
% 1.53/1.24 tff(143,plain,
% 1.53/1.24 (neq(V!48, nil)),
% 1.53/1.24 inference(and_elim,[status(thm)],[35])).
% 1.53/1.24 tff(144,plain,
% 1.53/1.24 (neq(X!50, nil)),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.53/1.24 tff(145,plain,
% 1.53/1.24 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 1.53/1.24 inference(tautology,[status(thm)],[])).
% 1.53/1.24 tff(146,plain,
% 1.53/1.24 (~(X!50 = nil)),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[145, 144, 138])).
% 1.53/1.24 tff(147,plain,
% 1.53/1.24 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(148,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[147])).
% 1.53/1.24 tff(149,plain,
% 1.53/1.24 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(150,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[149])).
% 1.53/1.24 tff(151,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.53/1.24 inference(transitivity,[status(thm)],[150, 148])).
% 1.53/1.24 tff(152,plain,
% 1.53/1.24 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(153,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[152])).
% 1.53/1.24 tff(154,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(155,plain,
% 1.53/1.24 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(156,plain,
% 1.53/1.24 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[155])).
% 1.53/1.24 tff(157,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 1.53/1.24 tff(158,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.53/1.24 tff(159,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[158, 154])).
% 1.53/1.24 tff(160,plain,(
% 1.53/1.24 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 1.53/1.24 inference(skolemize,[status(sab)],[159])).
% 1.53/1.24 tff(161,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[160, 153])).
% 1.53/1.24 tff(162,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[161, 151])).
% 1.53/1.24 tff(163,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(164,plain,
% 1.53/1.24 (((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) <=> ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(165,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))))),
% 1.53/1.24 inference(monotonicity,[status(thm)],[164])).
% 1.53/1.24 tff(166,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.53/1.24 inference(transitivity,[status(thm)],[165, 163])).
% 1.53/1.24 tff(167,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(168,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.53/1.24 tff(169,plain,
% 1.53/1.24 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[168, 162, 116])).
% 1.53/1.24 tff(170,plain,
% 1.53/1.24 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(171,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[170])).
% 1.53/1.24 tff(172,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(173,plain,
% 1.53/1.24 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(174,plain,
% 1.53/1.24 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(quant_intro,[status(thm)],[173])).
% 1.53/1.24 tff(175,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 1.53/1.24 tff(176,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.53/1.24 tff(177,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.53/1.24 tff(178,plain,(
% 1.53/1.24 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(skolemize,[status(sab)],[177])).
% 1.53/1.24 tff(179,plain,
% 1.53/1.24 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.53/1.24 tff(180,plain,
% 1.53/1.24 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(181,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 1.53/1.24 inference(quant_inst,[status(thm)],[])).
% 1.53/1.24 tff(182,plain,
% 1.53/1.24 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 1.53/1.24 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.53/1.24 tff(183,plain,
% 1.53/1.24 (segmentP(X!50, nil)),
% 1.53/1.24 inference(unit_resolution,[status(thm)],[182, 179, 116])).
% 1.53/1.24 tff(184,plain,
% 1.53/1.24 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(185,plain,
% 1.53/1.24 (((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50))) <=> ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(186,plain,
% 1.53/1.24 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))))),
% 1.53/1.24 inference(monotonicity,[status(thm)],[185])).
% 1.53/1.24 tff(187,plain,
% 1.53/1.24 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 1.53/1.25 inference(transitivity,[status(thm)],[186, 184])).
% 1.53/1.25 tff(188,plain,
% 1.53/1.25 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))),
% 1.53/1.25 inference(quant_inst,[status(thm)],[])).
% 1.53/1.25 tff(189,plain,
% 1.53/1.25 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))),
% 1.53/1.25 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.53/1.25 tff(190,plain,
% 1.53/1.25 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[189, 74, 183, 169])).
% 1.53/1.25 tff(191,plain,
% 1.53/1.25 (~segmentP(nil, X!50)),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[190, 146])).
% 1.53/1.25 tff(192,plain,
% 1.53/1.25 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 1.53/1.25 inference(tautology,[status(thm)],[])).
% 1.53/1.25 tff(193,plain,
% 1.53/1.25 (~(nil = X!50)),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[192, 191, 130])).
% 1.53/1.25 tff(194,plain,
% 1.53/1.25 ((~(~((nil = X!50) | (~(nil = W!49))))) <=> ((nil = X!50) | (~(nil = W!49)))),
% 1.53/1.25 inference(rewrite,[status(thm)],[])).
% 1.53/1.25 tff(195,plain,
% 1.53/1.25 (((~(nil = X!50)) & (nil = W!49)) <=> (~((nil = X!50) | (~(nil = W!49))))),
% 1.53/1.25 inference(rewrite,[status(thm)],[])).
% 1.53/1.25 tff(196,plain,
% 1.53/1.25 ((~((~(nil = X!50)) & (nil = W!49))) <=> (~(~((nil = X!50) | (~(nil = W!49)))))),
% 1.53/1.25 inference(monotonicity,[status(thm)],[195])).
% 1.53/1.25 tff(197,plain,
% 1.53/1.25 ((~((~(nil = X!50)) & (nil = W!49))) <=> ((nil = X!50) | (~(nil = W!49)))),
% 1.53/1.25 inference(transitivity,[status(thm)],[196, 194])).
% 1.53/1.25 tff(198,plain,
% 1.53/1.25 (~((~(nil = X!50)) & (nil = W!49))),
% 1.53/1.25 inference(and_elim,[status(thm)],[35])).
% 1.53/1.25 tff(199,plain,
% 1.53/1.25 ((nil = X!50) | (~(nil = W!49))),
% 1.53/1.25 inference(modus_ponens,[status(thm)],[198, 197])).
% 1.53/1.25 tff(200,plain,
% 1.53/1.25 (~(nil = W!49)),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[199, 193])).
% 1.53/1.25 tff(201,plain,
% 1.53/1.25 ((~((nil = app(nil, W!49)) <=> (nil = W!49))) | (~(nil = app(nil, W!49))) | (nil = W!49)),
% 1.53/1.25 inference(tautology,[status(thm)],[])).
% 1.53/1.25 tff(202,plain,
% 1.53/1.25 (~(nil = app(nil, W!49))),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[201, 200, 115])).
% 1.53/1.25 tff(203,plain,
% 1.53/1.25 ($false),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[202, 88])).
% 1.53/1.25 % SZS output end Proof
%------------------------------------------------------------------------------