TSTP Solution File: SWC339+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC339+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 11:57:13 EDT 2022
% Result : Theorem 12.88s 8.51s
% Output : Proof 12.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC339+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 00:09:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 12.88/8.51 % SZS status Theorem
% 12.88/8.51 % SZS output start Proof
% 12.88/8.51 tff(segmentP_type, type, (
% 12.88/8.51 segmentP: ( $i * $i ) > $o)).
% 12.88/8.51 tff(tptp_fun_W_49_type, type, (
% 12.88/8.51 tptp_fun_W_49: $i)).
% 12.88/8.51 tff(app_type, type, (
% 12.88/8.51 app: ( $i * $i ) > $i)).
% 12.88/8.51 tff(tptp_fun_Z_52_type, type, (
% 12.88/8.51 tptp_fun_Z_52: $i)).
% 12.88/8.51 tff(tptp_fun_Y_51_type, type, (
% 12.88/8.51 tptp_fun_Y_51: $i)).
% 12.88/8.51 tff(tptp_fun_U_47_type, type, (
% 12.88/8.51 tptp_fun_U_47: $i)).
% 12.88/8.51 tff(tptp_fun_V_48_type, type, (
% 12.88/8.51 tptp_fun_V_48: $i)).
% 12.88/8.51 tff(leq_type, type, (
% 12.88/8.51 leq: ( $i * $i ) > $o)).
% 12.88/8.51 tff(cons_type, type, (
% 12.88/8.51 cons: ( $i * $i ) > $i)).
% 12.88/8.51 tff(nil_type, type, (
% 12.88/8.51 nil: $i)).
% 12.88/8.51 tff(ssList_type, type, (
% 12.88/8.51 ssList: $i > $o)).
% 12.88/8.51 tff(ssItem_type, type, (
% 12.88/8.51 ssItem: $i > $o)).
% 12.88/8.51 tff(tptp_fun_X_50_type, type, (
% 12.88/8.51 tptp_fun_X_50: $i)).
% 12.88/8.51 tff(totalorderedP_type, type, (
% 12.88/8.51 totalorderedP: $i > $o)).
% 12.88/8.51 tff(1,plain,
% 12.88/8.51 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.51 inference(rewrite,[status(thm)],[])).
% 12.88/8.51 tff(2,plain,
% 12.88/8.51 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.51 inference(rewrite,[status(thm)],[])).
% 12.88/8.51 tff(3,plain,
% 12.88/8.51 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(4,plain,
% 12.88/8.52 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(5,plain,
% 12.88/8.52 ((ssList(Y!51) & (totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> (ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(6,plain,
% 12.88/8.52 (((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))) <=> (totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(7,plain,
% 12.88/8.52 ((~(~ssList(Y!51))) <=> ssList(Y!51)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(8,plain,
% 12.88/8.52 (((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> (ssList(Y!51) & (totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))),
% 12.88/8.52 inference(monotonicity,[status(thm)],[7, 6])).
% 12.88/8.52 tff(9,plain,
% 12.88/8.52 (((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))) <=> (ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(transitivity,[status(thm)],[8, 5])).
% 12.88/8.52 tff(10,plain,
% 12.88/8.52 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(11,plain,
% 12.88/8.52 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(12,plain,
% 12.88/8.52 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(13,plain,
% 12.88/8.52 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))),
% 12.88/8.52 inference(monotonicity,[status(thm)],[12, 11, 10, 9])).
% 12.88/8.52 tff(14,plain,
% 12.88/8.52 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(transitivity,[status(thm)],[13, 4])).
% 12.88/8.52 tff(15,plain,
% 12.88/8.52 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(16,plain,
% 12.88/8.52 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))),
% 12.88/8.52 inference(monotonicity,[status(thm)],[15, 14])).
% 12.88/8.52 tff(17,plain,
% 12.88/8.52 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(transitivity,[status(thm)],[16, 3])).
% 12.88/8.52 tff(18,plain,
% 12.88/8.52 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(19,plain,
% 12.88/8.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))),
% 12.88/8.52 inference(monotonicity,[status(thm)],[18, 17])).
% 12.88/8.52 tff(20,plain,
% 12.88/8.52 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(transitivity,[status(thm)],[19, 2])).
% 12.88/8.52 tff(21,plain,
% 12.88/8.52 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(22,plain,
% 12.88/8.52 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))))),
% 12.88/8.52 inference(monotonicity,[status(thm)],[21, 20])).
% 12.88/8.52 tff(23,plain,
% 12.88/8.52 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~ssList(Y!51))) & ((~(~totalorderedP(W!49))) & (~(~(app(app(Y!51, W!49), Z!52) = X!50))) & (~(~ssList(Z!52))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5)))))))),
% 12.88/8.52 inference(transitivity,[status(thm)],[22, 1])).
% 12.88/8.52 tff(24,plain,
% 12.88/8.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5))))))))))))),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(25,plain,
% 12.88/8.52 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~totalorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = W)) & leq(X1, X3)))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(cons(X5, nil), X6) = Z)) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : ((ssList(X8) & (app(X8, cons(X7, nil)) = W)) & leq(X7, X5))))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & totalorderedP(U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5))))))))))))),
% 12.88/8.52 inference(rewrite,[status(thm)],[])).
% 12.88/8.52 tff(26,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~totalorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = W)) & leq(X1, X3)))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(cons(X5, nil), X6) = Z)) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : ((ssList(X8) & (app(X8, cons(X7, nil)) = W)) & leq(X7, X5))))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & totalorderedP(U)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 12.88/8.52 tff(27,plain,
% 12.88/8.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.52 inference(modus_ponens,[status(thm)],[26, 25])).
% 12.88/8.52 tff(28,plain,
% 12.88/8.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.52 inference(modus_ponens,[status(thm)],[27, 24])).
% 12.88/8.52 tff(29,plain,
% 12.88/8.52 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[28, 24])).
% 12.88/8.53 tff(30,plain,
% 12.88/8.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[29, 24])).
% 12.88/8.53 tff(31,plain,
% 12.88/8.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[30, 24])).
% 12.88/8.53 tff(32,plain,
% 12.88/8.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[31, 24])).
% 12.88/8.53 tff(33,plain,
% 12.88/8.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & totalorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(W)) | (~(app(app(Y, W), Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = W) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = W) & leq(X7, X5)))))))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[32, 24])).
% 12.88/8.53 tff(34,plain,
% 12.88/8.53 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & totalorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ssList(Y!51) & totalorderedP(W!49) & (app(app(Y!51, W!49), Z!52) = X!50) & ssList(Z!52) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = W!49) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!52)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = W!49) & leq(X7, X5))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[33, 23])).
% 12.88/8.53 tff(35,plain,
% 12.88/8.53 (U!47 = W!49),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(36,plain,
% 12.88/8.53 (W!49 = U!47),
% 12.88/8.53 inference(symmetry,[status(thm)],[35])).
% 12.88/8.53 tff(37,plain,
% 12.88/8.53 (V!48 = X!50),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(38,plain,
% 12.88/8.53 (X!50 = V!48),
% 12.88/8.53 inference(symmetry,[status(thm)],[37])).
% 12.88/8.53 tff(39,plain,
% 12.88/8.53 (app(app(Y!51, W!49), Z!52) = X!50),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(40,plain,
% 12.88/8.53 (app(app(Y!51, W!49), Z!52) = V!48),
% 12.88/8.53 inference(transitivity,[status(thm)],[39, 38])).
% 12.88/8.53 tff(41,plain,
% 12.88/8.53 (segmentP(app(app(Y!51, W!49), Z!52), W!49) <=> segmentP(V!48, U!47)),
% 12.88/8.53 inference(monotonicity,[status(thm)],[40, 36])).
% 12.88/8.53 tff(42,plain,
% 12.88/8.53 (segmentP(V!48, U!47) <=> segmentP(app(app(Y!51, W!49), Z!52), W!49)),
% 12.88/8.53 inference(symmetry,[status(thm)],[41])).
% 12.88/8.53 tff(43,plain,
% 12.88/8.53 ((~segmentP(V!48, U!47)) <=> (~segmentP(app(app(Y!51, W!49), Z!52), W!49))),
% 12.88/8.53 inference(monotonicity,[status(thm)],[42])).
% 12.88/8.53 tff(44,plain,
% 12.88/8.53 (totalorderedP(U!47) <=> totalorderedP(W!49)),
% 12.88/8.53 inference(monotonicity,[status(thm)],[35])).
% 12.88/8.53 tff(45,plain,
% 12.88/8.53 (totalorderedP(W!49) <=> totalorderedP(U!47)),
% 12.88/8.53 inference(symmetry,[status(thm)],[44])).
% 12.88/8.53 tff(46,plain,
% 12.88/8.53 (totalorderedP(W!49)),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(47,plain,
% 12.88/8.53 (totalorderedP(U!47)),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[46, 45])).
% 12.88/8.53 tff(48,plain,
% 12.88/8.53 ((~(~((~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))) <=> ((~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(49,plain,
% 12.88/8.53 ((segmentP(V!48, U!47) & totalorderedP(U!47)) <=> (~((~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(50,plain,
% 12.88/8.53 ((~(segmentP(V!48, U!47) & totalorderedP(U!47))) <=> (~(~((~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))))),
% 12.88/8.53 inference(monotonicity,[status(thm)],[49])).
% 12.88/8.53 tff(51,plain,
% 12.88/8.53 ((~(segmentP(V!48, U!47) & totalorderedP(U!47))) <=> ((~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))),
% 12.88/8.53 inference(transitivity,[status(thm)],[50, 48])).
% 12.88/8.53 tff(52,plain,
% 12.88/8.53 (~(segmentP(V!48, U!47) & totalorderedP(U!47))),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(53,plain,
% 12.88/8.53 ((~segmentP(V!48, U!47)) | (~totalorderedP(U!47))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[52, 51])).
% 12.88/8.53 tff(54,plain,
% 12.88/8.53 (~segmentP(V!48, U!47)),
% 12.88/8.53 inference(unit_resolution,[status(thm)],[53, 47])).
% 12.88/8.53 tff(55,plain,
% 12.88/8.53 (~segmentP(app(app(Y!51, W!49), Z!52), W!49)),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[54, 43])).
% 12.88/8.53 tff(56,plain,
% 12.88/8.53 (ssList(W!49)),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(57,plain,
% 12.88/8.53 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 12.88/8.53 inference(bind,[status(th)],[])).
% 12.88/8.53 tff(58,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(quant_intro,[status(thm)],[57])).
% 12.88/8.53 tff(59,plain,
% 12.88/8.53 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 12.88/8.53 inference(bind,[status(th)],[])).
% 12.88/8.53 tff(60,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(quant_intro,[status(thm)],[59])).
% 12.88/8.53 tff(61,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(transitivity,[status(thm)],[60, 58])).
% 12.88/8.53 tff(62,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(63,plain,
% 12.88/8.53 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((segmentP(U, V) => segmentP(app(app(W, U), X), V)) <=> ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))))), rewrite((ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), (![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> (ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), rewrite((ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), (![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))))),
% 12.88/8.53 inference(bind,[status(th)],[])).
% 12.88/8.53 tff(64,plain,
% 12.88/8.53 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(quant_intro,[status(thm)],[63])).
% 12.88/8.53 tff(65,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax56')).
% 12.88/8.53 tff(66,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[65, 64])).
% 12.88/8.53 tff(67,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[66, 62])).
% 12.88/8.53 tff(68,plain,(
% 12.88/8.53 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(skolemize,[status(sab)],[67])).
% 12.88/8.53 tff(69,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[68, 61])).
% 12.88/8.53 tff(70,plain,
% 12.88/8.53 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(71,plain,
% 12.88/8.53 (((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V)))))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(72,plain,
% 12.88/8.53 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))))),
% 12.88/8.53 inference(monotonicity,[status(thm)],[71])).
% 12.88/8.53 tff(73,plain,
% 12.88/8.53 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 12.88/8.53 inference(transitivity,[status(thm)],[72, 70])).
% 12.88/8.53 tff(74,plain,
% 12.88/8.53 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))),
% 12.88/8.53 inference(quant_inst,[status(thm)],[])).
% 12.88/8.53 tff(75,plain,
% 12.88/8.53 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[74, 73])).
% 12.88/8.53 tff(76,plain,
% 12.88/8.53 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 12.88/8.53 inference(unit_resolution,[status(thm)],[75, 69, 56])).
% 12.88/8.53 tff(77,plain,
% 12.88/8.53 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(78,plain,
% 12.88/8.53 (((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49))))) <=> ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(79,plain,
% 12.88/8.53 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))))),
% 12.88/8.53 inference(monotonicity,[status(thm)],[78])).
% 12.88/8.53 tff(80,plain,
% 12.88/8.53 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 12.88/8.53 inference(transitivity,[status(thm)],[79, 77])).
% 12.88/8.53 tff(81,plain,
% 12.88/8.53 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))),
% 12.88/8.53 inference(quant_inst,[status(thm)],[])).
% 12.88/8.53 tff(82,plain,
% 12.88/8.53 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[81, 80])).
% 12.88/8.53 tff(83,plain,
% 12.88/8.53 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 12.88/8.53 inference(unit_resolution,[status(thm)],[82, 56, 76])).
% 12.88/8.53 tff(84,plain,
% 12.88/8.53 (ssList(Y!51)),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(85,plain,
% 12.88/8.53 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(Y!51)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49)))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(Y!51)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49)))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(86,plain,
% 12.88/8.53 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(Y!51)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49)))),
% 12.88/8.53 inference(quant_inst,[status(thm)],[])).
% 12.88/8.53 tff(87,plain,
% 12.88/8.53 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(Y!51)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[86, 85])).
% 12.88/8.53 tff(88,plain,
% 12.88/8.53 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49))),
% 12.88/8.53 inference(unit_resolution,[status(thm)],[87, 84, 83])).
% 12.88/8.53 tff(89,plain,
% 12.88/8.53 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 12.88/8.53 inference(bind,[status(th)],[])).
% 12.88/8.53 tff(90,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(quant_intro,[status(thm)],[89])).
% 12.88/8.53 tff(91,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(92,plain,
% 12.88/8.53 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 12.88/8.53 inference(bind,[status(th)],[])).
% 12.88/8.53 tff(93,plain,
% 12.88/8.53 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(quant_intro,[status(thm)],[92])).
% 12.88/8.53 tff(94,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax55')).
% 12.88/8.53 tff(95,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[94, 93])).
% 12.88/8.53 tff(96,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[95, 91])).
% 12.88/8.53 tff(97,plain,(
% 12.88/8.53 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(skolemize,[status(sab)],[96])).
% 12.88/8.53 tff(98,plain,
% 12.88/8.53 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[97, 90])).
% 12.88/8.53 tff(99,plain,
% 12.88/8.53 (((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49))),
% 12.88/8.53 inference(rewrite,[status(thm)],[])).
% 12.88/8.53 tff(100,plain,
% 12.88/8.53 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 12.88/8.53 inference(quant_inst,[status(thm)],[])).
% 12.88/8.53 tff(101,plain,
% 12.88/8.53 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 12.88/8.53 inference(modus_ponens,[status(thm)],[100, 99])).
% 12.88/8.53 tff(102,plain,
% 12.88/8.53 (segmentP(W!49, W!49)),
% 12.88/8.53 inference(unit_resolution,[status(thm)],[101, 98, 56])).
% 12.88/8.53 tff(103,plain,
% 12.88/8.53 (ssList(Z!52)),
% 12.88/8.53 inference(and_elim,[status(thm)],[34])).
% 12.88/8.53 tff(104,plain,
% 12.88/8.53 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49))) | ((~ssList(Z!52)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), Z!52), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49))) | (~ssList(Z!52)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), Z!52), W!49))),
% 12.90/8.55 inference(rewrite,[status(thm)],[])).
% 12.90/8.55 tff(105,plain,
% 12.90/8.55 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49))) | ((~ssList(Z!52)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), Z!52), W!49))),
% 12.90/8.55 inference(quant_inst,[status(thm)],[])).
% 12.90/8.55 tff(106,plain,
% 12.90/8.55 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), X), W!49))) | (~ssList(Z!52)) | (~segmentP(W!49, W!49)) | segmentP(app(app(Y!51, W!49), Z!52), W!49)),
% 12.90/8.55 inference(modus_ponens,[status(thm)],[105, 104])).
% 12.90/8.55 tff(107,plain,
% 12.90/8.55 (segmentP(app(app(Y!51, W!49), Z!52), W!49)),
% 12.90/8.55 inference(unit_resolution,[status(thm)],[106, 103, 102, 88])).
% 12.90/8.55 tff(108,plain,
% 12.90/8.55 ($false),
% 12.90/8.55 inference(unit_resolution,[status(thm)],[107, 55])).
% 12.90/8.55 % SZS output end Proof
%------------------------------------------------------------------------------