TSTP Solution File: SWC092+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC092+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 11:55:12 EDT 2022
% Result : Theorem 9.51s 6.35s
% Output : Proof 9.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC092+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 21:50:07 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.
% 9.51/6.35 % SZS status Theorem
% 9.51/6.35 % SZS output start Proof
% 9.51/6.35 tff(segmentP_type, type, (
% 9.51/6.35 segmentP: ( $i * $i ) > $o)).
% 9.51/6.35 tff(tptp_fun_W_49_type, type, (
% 9.51/6.35 tptp_fun_W_49: $i)).
% 9.51/6.35 tff(app_type, type, (
% 9.51/6.35 app: ( $i * $i ) > $i)).
% 9.51/6.35 tff(tptp_fun_Z_51_type, type, (
% 9.51/6.35 tptp_fun_Z_51: $i)).
% 9.51/6.35 tff(nil_type, type, (
% 9.51/6.35 nil: $i)).
% 9.51/6.35 tff(tptp_fun_V_48_type, type, (
% 9.51/6.35 tptp_fun_V_48: $i)).
% 9.51/6.35 tff(tptp_fun_X_50_type, type, (
% 9.51/6.35 tptp_fun_X_50: $i)).
% 9.51/6.35 tff(lt_type, type, (
% 9.51/6.35 lt: ( $i * $i ) > $o)).
% 9.51/6.35 tff(cons_type, type, (
% 9.51/6.35 cons: ( $i * $i ) > $i)).
% 9.51/6.35 tff(ssList_type, type, (
% 9.51/6.35 ssList: $i > $o)).
% 9.51/6.35 tff(ssItem_type, type, (
% 9.51/6.35 ssItem: $i > $o)).
% 9.51/6.35 tff(strictorderedP_type, type, (
% 9.51/6.35 strictorderedP: $i > $o)).
% 9.51/6.35 tff(tptp_fun_U_47_type, type, (
% 9.51/6.35 tptp_fun_U_47: $i)).
% 9.51/6.35 tff(neq_type, type, (
% 9.51/6.35 neq: ( $i * $i ) > $o)).
% 9.51/6.35 tff(1,plain,
% 9.51/6.35 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(2,plain,
% 9.51/6.35 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(3,plain,
% 9.51/6.35 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(4,plain,
% 9.51/6.35 (((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & (strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(5,plain,
% 9.51/6.35 (((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))) <=> (strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(6,plain,
% 9.51/6.35 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(7,plain,
% 9.51/6.35 ((~(~neq(V!48, nil))) <=> neq(V!48, nil)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(8,plain,
% 9.51/6.35 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(9,plain,
% 9.51/6.35 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(10,plain,
% 9.51/6.35 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & (strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))),
% 9.51/6.35 inference(monotonicity,[status(thm)],[9, 8, 7, 6, 5])).
% 9.51/6.35 tff(11,plain,
% 9.51/6.35 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(transitivity,[status(thm)],[10, 4])).
% 9.51/6.35 tff(12,plain,
% 9.51/6.35 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(13,plain,
% 9.51/6.35 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))),
% 9.51/6.35 inference(monotonicity,[status(thm)],[12, 11])).
% 9.51/6.35 tff(14,plain,
% 9.51/6.35 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(transitivity,[status(thm)],[13, 3])).
% 9.51/6.35 tff(15,plain,
% 9.51/6.35 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(16,plain,
% 9.51/6.35 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))),
% 9.51/6.35 inference(monotonicity,[status(thm)],[15, 14])).
% 9.51/6.35 tff(17,plain,
% 9.51/6.35 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(transitivity,[status(thm)],[16, 2])).
% 9.51/6.35 tff(18,plain,
% 9.51/6.35 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(19,plain,
% 9.51/6.35 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))),
% 9.51/6.35 inference(monotonicity,[status(thm)],[18, 17])).
% 9.51/6.35 tff(20,plain,
% 9.51/6.35 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Z!51) = X!50))) & (~(~ssList(Z!51))) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1)))))))),
% 9.51/6.35 inference(transitivity,[status(thm)],[19, 1])).
% 9.51/6.35 tff(21,plain,
% 9.51/6.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1)))))))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(22,plain,
% 9.51/6.35 ((~![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) & neq(Y, nil)) & segmentP(V, Y)) & segmentP(U, Y))) | ![Z: $i] : (ssList(Z) => (((~(app(W, Z) = X)) | (~strictorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(cons(X1, nil), X2) = Z)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(X4, cons(X3, nil)) = W)) & lt(X3, X1)))))))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1)))))))))))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(23,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) & neq(Y, nil)) & segmentP(V, Y)) & segmentP(U, Y))) | ![Z: $i] : (ssList(Z) => (((~(app(W, Z) = X)) | (~strictorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(cons(X1, nil), X2) = Z)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(X4, cons(X3, nil)) = W)) & lt(X3, X1)))))))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 9.51/6.35 tff(24,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[23, 22])).
% 9.51/6.35 tff(25,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[24, 21])).
% 9.51/6.35 tff(26,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[25, 21])).
% 9.51/6.35 tff(27,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[26, 21])).
% 9.51/6.35 tff(28,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[27, 21])).
% 9.51/6.35 tff(29,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[28, 21])).
% 9.51/6.35 tff(30,plain,
% 9.51/6.35 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)) | ![Z: $i] : ((~strictorderedP(W)) | (~(app(W, Z) = X)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(cons(X1, nil), X2) = Z) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(X4, cons(X3, nil)) = W) & lt(X3, X1))))))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[29, 21])).
% 9.51/6.35 tff(31,plain,
% 9.51/6.35 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) & strictorderedP(W!49) & (app(W!49, Z!51) = X!50) & ssList(Z!51) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(cons(X1, nil), X2) = Z!51)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(X4, cons(X3, nil)) = W!49) & lt(X3, X1))))))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[30, 20])).
% 9.51/6.35 tff(32,plain,
% 9.51/6.35 (V!48 = X!50),
% 9.51/6.35 inference(and_elim,[status(thm)],[31])).
% 9.51/6.35 tff(33,plain,
% 9.51/6.35 (X!50 = V!48),
% 9.51/6.35 inference(symmetry,[status(thm)],[32])).
% 9.51/6.35 tff(34,plain,
% 9.51/6.35 (app(W!49, Z!51) = X!50),
% 9.51/6.35 inference(and_elim,[status(thm)],[31])).
% 9.51/6.35 tff(35,plain,
% 9.51/6.35 (ssList(W!49)),
% 9.51/6.35 inference(and_elim,[status(thm)],[31])).
% 9.51/6.35 tff(36,plain,
% 9.51/6.35 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 9.51/6.35 inference(bind,[status(th)],[])).
% 9.51/6.35 tff(37,plain,
% 9.51/6.35 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(quant_intro,[status(thm)],[36])).
% 9.51/6.35 tff(38,plain,
% 9.51/6.35 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(39,plain,
% 9.51/6.35 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 9.51/6.35 inference(bind,[status(th)],[])).
% 9.51/6.35 tff(40,plain,
% 9.51/6.35 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(quant_intro,[status(thm)],[39])).
% 9.51/6.35 tff(41,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 9.51/6.35 tff(42,plain,
% 9.51/6.35 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[41, 40])).
% 9.51/6.35 tff(43,plain,
% 9.51/6.35 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[42, 38])).
% 9.51/6.35 tff(44,plain,(
% 9.51/6.35 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(skolemize,[status(sab)],[43])).
% 9.51/6.35 tff(45,plain,
% 9.51/6.35 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.51/6.35 inference(modus_ponens,[status(thm)],[44, 37])).
% 9.51/6.35 tff(46,plain,
% 9.51/6.35 (((~![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))),
% 9.51/6.35 inference(rewrite,[status(thm)],[])).
% 9.51/6.35 tff(47,plain,
% 9.51/6.35 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 9.51/6.35 inference(quant_inst,[status(thm)],[])).
% 9.51/6.35 tff(48,plain,
% 9.51/6.35 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[47, 46])).
% 9.51/6.36 tff(49,plain,
% 9.51/6.36 (app(nil, W!49) = W!49),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 9.51/6.36 tff(50,plain,
% 9.51/6.36 (app(app(nil, W!49), Z!51) = app(W!49, Z!51)),
% 9.51/6.36 inference(monotonicity,[status(thm)],[49])).
% 9.51/6.36 tff(51,plain,
% 9.51/6.36 (app(app(nil, W!49), Z!51) = V!48),
% 9.51/6.36 inference(transitivity,[status(thm)],[50, 34, 33])).
% 9.51/6.36 tff(52,plain,
% 9.51/6.36 (segmentP(app(app(nil, W!49), Z!51), W!49) <=> segmentP(V!48, W!49)),
% 9.51/6.36 inference(monotonicity,[status(thm)],[51])).
% 9.51/6.36 tff(53,plain,
% 9.51/6.36 (segmentP(V!48, W!49) <=> segmentP(app(app(nil, W!49), Z!51), W!49)),
% 9.51/6.36 inference(symmetry,[status(thm)],[52])).
% 9.51/6.36 tff(54,plain,
% 9.51/6.36 ((~segmentP(V!48, W!49)) <=> (~segmentP(app(app(nil, W!49), Z!51), W!49))),
% 9.51/6.36 inference(monotonicity,[status(thm)],[53])).
% 9.51/6.36 tff(55,plain,
% 9.51/6.36 (U!47 = W!49),
% 9.51/6.36 inference(and_elim,[status(thm)],[31])).
% 9.51/6.36 tff(56,plain,
% 9.51/6.36 (W!49 = U!47),
% 9.51/6.36 inference(symmetry,[status(thm)],[55])).
% 9.51/6.36 tff(57,plain,
% 9.51/6.36 (segmentP(W!49, W!49) <=> segmentP(U!47, W!49)),
% 9.51/6.36 inference(monotonicity,[status(thm)],[56])).
% 9.51/6.36 tff(58,plain,
% 9.51/6.36 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(59,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[58])).
% 9.51/6.36 tff(60,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(61,plain,
% 9.51/6.36 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(62,plain,
% 9.51/6.36 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[61])).
% 9.51/6.36 tff(63,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax55')).
% 9.51/6.36 tff(64,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[63, 62])).
% 9.51/6.36 tff(65,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[64, 60])).
% 9.51/6.36 tff(66,plain,(
% 9.51/6.36 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(skolemize,[status(sab)],[65])).
% 9.51/6.36 tff(67,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[66, 59])).
% 9.51/6.36 tff(68,plain,
% 9.51/6.36 (((~![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))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(69,plain,
% 9.51/6.36 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(70,plain,
% 9.51/6.36 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[69, 68])).
% 9.51/6.36 tff(71,plain,
% 9.51/6.36 (segmentP(W!49, W!49)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[70, 67, 35])).
% 9.51/6.36 tff(72,plain,
% 9.51/6.36 (segmentP(U!47, W!49)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[71, 57])).
% 9.51/6.36 tff(73,plain,
% 9.51/6.36 (^[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))))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(74,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[73])).
% 9.51/6.36 tff(75,plain,
% 9.51/6.36 (^[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))))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(76,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[75])).
% 9.51/6.36 tff(77,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(transitivity,[status(thm)],[76, 74])).
% 9.51/6.36 tff(78,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(79,plain,
% 9.51/6.36 (^[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)))))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(80,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[79])).
% 9.51/6.36 tff(81,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 9.51/6.36 tff(82,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[81, 80])).
% 9.51/6.36 tff(83,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[82, 78])).
% 9.51/6.36 tff(84,plain,(
% 9.51/6.36 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 9.51/6.36 inference(skolemize,[status(sab)],[83])).
% 9.51/6.36 tff(85,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[84, 77])).
% 9.51/6.36 tff(86,plain,
% 9.51/6.36 (((~![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)))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(87,plain,
% 9.51/6.36 ((~![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)))))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(88,plain,
% 9.51/6.36 ((~![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))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[87, 86])).
% 9.51/6.36 tff(89,plain,
% 9.51/6.36 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[88, 85, 35])).
% 9.51/6.36 tff(90,plain,
% 9.51/6.36 (ssList(nil) <=> ssList(nil)),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(91,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 9.51/6.36 tff(92,plain,
% 9.51/6.36 (ssList(nil)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[91, 90])).
% 9.51/6.36 tff(93,plain,
% 9.51/6.36 (((~![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))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(94,plain,
% 9.51/6.36 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(95,plain,
% 9.51/6.36 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[94, 93])).
% 9.51/6.36 tff(96,plain,
% 9.51/6.36 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[95, 92, 89])).
% 9.51/6.36 tff(97,plain,
% 9.51/6.36 ((W!49 = nil) <=> (nil = W!49)),
% 9.51/6.36 inference(commutativity,[status(thm)],[])).
% 9.51/6.36 tff(98,plain,
% 9.51/6.36 ((nil = W!49) <=> (W!49 = nil)),
% 9.51/6.36 inference(symmetry,[status(thm)],[97])).
% 9.51/6.36 tff(99,plain,
% 9.51/6.36 ((~(nil = W!49)) <=> (~(W!49 = nil))),
% 9.51/6.36 inference(monotonicity,[status(thm)],[98])).
% 9.51/6.36 tff(100,plain,
% 9.51/6.36 (ssList(X!50)),
% 9.51/6.36 inference(and_elim,[status(thm)],[31])).
% 9.51/6.36 tff(101,plain,
% 9.51/6.36 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(102,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[101])).
% 9.51/6.36 tff(103,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(104,plain,
% 9.51/6.36 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(105,plain,
% 9.51/6.36 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[104])).
% 9.51/6.36 tff(106,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 9.51/6.36 tff(107,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[106, 105])).
% 9.51/6.36 tff(108,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[107, 103])).
% 9.51/6.36 tff(109,plain,(
% 9.51/6.36 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(skolemize,[status(sab)],[108])).
% 9.51/6.36 tff(110,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[109, 102])).
% 9.51/6.36 tff(111,plain,
% 9.51/6.36 (((~![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)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(112,plain,
% 9.51/6.36 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(113,plain,
% 9.51/6.36 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[112, 111])).
% 9.51/6.36 tff(114,plain,
% 9.51/6.36 (segmentP(nil, X!50) <=> (nil = X!50)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 9.51/6.36 tff(115,plain,
% 9.51/6.36 (((~![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)))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(116,plain,
% 9.51/6.36 ((~![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)))))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(117,plain,
% 9.51/6.36 ((~![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))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[116, 115])).
% 9.51/6.36 tff(118,plain,
% 9.51/6.36 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[117, 85, 100])).
% 9.51/6.36 tff(119,plain,
% 9.51/6.36 (((~![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))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(120,plain,
% 9.51/6.36 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(121,plain,
% 9.51/6.36 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[120, 119])).
% 9.51/6.36 tff(122,plain,
% 9.51/6.36 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[121, 92, 118])).
% 9.51/6.36 tff(123,plain,
% 9.51/6.36 (neq(X!50, nil) <=> neq(V!48, nil)),
% 9.51/6.36 inference(monotonicity,[status(thm)],[33])).
% 9.51/6.36 tff(124,plain,
% 9.51/6.36 (neq(V!48, nil) <=> neq(X!50, nil)),
% 9.51/6.36 inference(symmetry,[status(thm)],[123])).
% 9.51/6.36 tff(125,plain,
% 9.51/6.36 (neq(V!48, nil)),
% 9.51/6.36 inference(and_elim,[status(thm)],[31])).
% 9.51/6.36 tff(126,plain,
% 9.51/6.36 (neq(X!50, nil)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[125, 124])).
% 9.51/6.36 tff(127,plain,
% 9.51/6.36 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 9.51/6.36 inference(tautology,[status(thm)],[])).
% 9.51/6.36 tff(128,plain,
% 9.51/6.36 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~(X!50 = nil))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[127, 126])).
% 9.51/6.36 tff(129,plain,
% 9.51/6.36 (~(X!50 = nil)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[128, 122])).
% 9.51/6.36 tff(130,plain,
% 9.51/6.36 (^[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)))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(131,plain,
% 9.51/6.36 (![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))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[130])).
% 9.51/6.36 tff(132,plain,
% 9.51/6.36 (^[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)))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(133,plain,
% 9.51/6.36 (![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))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[132])).
% 9.51/6.36 tff(134,plain,
% 9.51/6.36 (![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))))),
% 9.51/6.36 inference(transitivity,[status(thm)],[133, 131])).
% 9.51/6.36 tff(135,plain,
% 9.51/6.36 (^[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)))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(136,plain,
% 9.51/6.36 (![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))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[135])).
% 9.51/6.36 tff(137,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(138,plain,
% 9.51/6.36 (^[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)))))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(139,plain,
% 9.51/6.36 (![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)))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[138])).
% 9.51/6.36 tff(140,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')).
% 9.51/6.36 tff(141,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[140, 139])).
% 9.51/6.36 tff(142,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[141, 137])).
% 9.51/6.36 tff(143,plain,(
% 9.51/6.36 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.51/6.36 inference(skolemize,[status(sab)],[142])).
% 9.51/6.36 tff(144,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[143, 136])).
% 9.51/6.36 tff(145,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[144, 134])).
% 9.51/6.36 tff(146,plain,
% 9.51/6.36 (((~![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))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(147,plain,
% 9.51/6.36 (((~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))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(148,plain,
% 9.51/6.36 (((~![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)))))),
% 9.51/6.36 inference(monotonicity,[status(thm)],[147])).
% 9.51/6.36 tff(149,plain,
% 9.51/6.36 (((~![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))))),
% 9.51/6.36 inference(transitivity,[status(thm)],[148, 146])).
% 9.51/6.36 tff(150,plain,
% 9.51/6.36 ((~![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))))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(151,plain,
% 9.51/6.36 ((~![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)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[150, 149])).
% 9.51/6.36 tff(152,plain,
% 9.51/6.36 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[151, 145, 100])).
% 9.51/6.36 tff(153,plain,
% 9.51/6.36 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(154,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[153])).
% 9.51/6.36 tff(155,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(156,plain,
% 9.51/6.36 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(157,plain,
% 9.51/6.36 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[156])).
% 9.51/6.36 tff(158,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 9.51/6.36 tff(159,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[158, 157])).
% 9.51/6.36 tff(160,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[159, 155])).
% 9.51/6.36 tff(161,plain,(
% 9.51/6.36 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(skolemize,[status(sab)],[160])).
% 9.51/6.36 tff(162,plain,
% 9.51/6.36 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[161, 154])).
% 9.51/6.36 tff(163,plain,
% 9.51/6.36 (((~![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))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(164,plain,
% 9.51/6.36 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(165,plain,
% 9.51/6.36 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[164, 163])).
% 9.51/6.36 tff(166,plain,
% 9.51/6.36 (segmentP(X!50, nil)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[165, 162, 100])).
% 9.51/6.36 tff(167,plain,
% 9.51/6.36 (((~![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)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(168,plain,
% 9.51/6.36 (((~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)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(169,plain,
% 9.51/6.36 (((~![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))))),
% 9.51/6.36 inference(monotonicity,[status(thm)],[168])).
% 9.51/6.36 tff(170,plain,
% 9.51/6.36 (((~![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)))),
% 9.51/6.36 inference(transitivity,[status(thm)],[169, 167])).
% 9.51/6.36 tff(171,plain,
% 9.51/6.36 ((~![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)))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(172,plain,
% 9.51/6.36 ((~![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))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[171, 170])).
% 9.51/6.36 tff(173,plain,
% 9.51/6.36 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[172, 92, 166, 152])).
% 9.51/6.36 tff(174,plain,
% 9.51/6.36 (~segmentP(nil, X!50)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[173, 129])).
% 9.51/6.36 tff(175,plain,
% 9.51/6.36 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 9.51/6.36 inference(tautology,[status(thm)],[])).
% 9.51/6.36 tff(176,plain,
% 9.51/6.36 (~(nil = X!50)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[175, 174, 114])).
% 9.51/6.36 tff(177,plain,
% 9.51/6.36 ((~(~((nil = X!50) | (~(nil = W!49))))) <=> ((nil = X!50) | (~(nil = W!49)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(178,plain,
% 9.51/6.36 (((~(nil = X!50)) & (nil = W!49)) <=> (~((nil = X!50) | (~(nil = W!49))))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(179,plain,
% 9.51/6.36 ((~((~(nil = X!50)) & (nil = W!49))) <=> (~(~((nil = X!50) | (~(nil = W!49)))))),
% 9.51/6.36 inference(monotonicity,[status(thm)],[178])).
% 9.51/6.36 tff(180,plain,
% 9.51/6.36 ((~((~(nil = X!50)) & (nil = W!49))) <=> ((nil = X!50) | (~(nil = W!49)))),
% 9.51/6.36 inference(transitivity,[status(thm)],[179, 177])).
% 9.51/6.36 tff(181,plain,
% 9.51/6.36 (~((~(nil = X!50)) & (nil = W!49))),
% 9.51/6.36 inference(and_elim,[status(thm)],[31])).
% 9.51/6.36 tff(182,plain,
% 9.51/6.36 ((nil = X!50) | (~(nil = W!49))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[181, 180])).
% 9.51/6.36 tff(183,plain,
% 9.51/6.36 (~(nil = W!49)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[182, 176])).
% 9.51/6.36 tff(184,plain,
% 9.51/6.36 (~(W!49 = nil)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[183, 99])).
% 9.51/6.36 tff(185,plain,
% 9.51/6.36 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 9.51/6.36 inference(tautology,[status(thm)],[])).
% 9.51/6.36 tff(186,plain,
% 9.51/6.36 (neq(W!49, nil)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[185, 184, 96])).
% 9.51/6.36 tff(187,plain,
% 9.51/6.36 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(188,plain,
% 9.51/6.36 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[187])).
% 9.51/6.36 tff(189,plain,
% 9.51/6.36 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(190,plain,
% 9.51/6.36 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[189])).
% 9.51/6.36 tff(191,plain,
% 9.51/6.36 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))),
% 9.51/6.36 inference(and_elim,[status(thm)],[31])).
% 9.51/6.36 tff(192,plain,
% 9.51/6.36 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[191, 190])).
% 9.51/6.36 tff(193,plain,
% 9.51/6.36 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[192, 188])).
% 9.51/6.36 tff(194,plain,
% 9.51/6.36 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~ssList(W!49)) | (~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(195,plain,
% 9.51/6.36 (((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49))) <=> ((~ssList(W!49)) | (~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)))),
% 9.51/6.36 inference(rewrite,[status(thm)],[])).
% 9.51/6.36 tff(196,plain,
% 9.51/6.36 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49))))),
% 9.51/6.36 inference(monotonicity,[status(thm)],[195])).
% 9.51/6.36 tff(197,plain,
% 9.51/6.36 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~ssList(W!49)) | (~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)))),
% 9.51/6.36 inference(transitivity,[status(thm)],[196, 194])).
% 9.51/6.36 tff(198,plain,
% 9.51/6.36 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49)))),
% 9.51/6.36 inference(quant_inst,[status(thm)],[])).
% 9.51/6.36 tff(199,plain,
% 9.51/6.36 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~ssList(W!49)) | (~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49))),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[198, 197])).
% 9.51/6.36 tff(200,plain,
% 9.51/6.36 ((~segmentP(V!48, W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49))),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[199, 35, 193])).
% 9.51/6.36 tff(201,plain,
% 9.51/6.36 (~segmentP(V!48, W!49)),
% 9.51/6.36 inference(unit_resolution,[status(thm)],[200, 186, 72])).
% 9.51/6.36 tff(202,plain,
% 9.51/6.36 (~segmentP(app(app(nil, W!49), Z!51), W!49)),
% 9.51/6.36 inference(modus_ponens,[status(thm)],[201, 54])).
% 9.51/6.36 tff(203,plain,
% 9.51/6.36 (^[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)))))))),
% 9.51/6.36 inference(bind,[status(th)],[])).
% 9.51/6.36 tff(204,plain,
% 9.51/6.36 (![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))))))),
% 9.51/6.36 inference(quant_intro,[status(thm)],[203])).
% 9.51/6.36 tff(205,plain,
% 9.51/6.36 (^[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)))))))),
% 9.51/6.37 inference(bind,[status(th)],[])).
% 9.51/6.37 tff(206,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(quant_intro,[status(thm)],[205])).
% 9.51/6.37 tff(207,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(transitivity,[status(thm)],[206, 204])).
% 9.51/6.37 tff(208,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(rewrite,[status(thm)],[])).
% 9.51/6.37 tff(209,plain,
% 9.51/6.37 (^[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))))))))),
% 9.51/6.37 inference(bind,[status(th)],[])).
% 9.51/6.37 tff(210,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(quant_intro,[status(thm)],[209])).
% 9.51/6.37 tff(211,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')).
% 9.51/6.37 tff(212,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(modus_ponens,[status(thm)],[211, 210])).
% 9.51/6.37 tff(213,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(modus_ponens,[status(thm)],[212, 208])).
% 9.51/6.37 tff(214,plain,(
% 9.51/6.37 ![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))))))),
% 9.51/6.37 inference(skolemize,[status(sab)],[213])).
% 9.51/6.37 tff(215,plain,
% 9.51/6.37 (![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))))))),
% 9.51/6.37 inference(modus_ponens,[status(thm)],[214, 207])).
% 9.51/6.37 tff(216,plain,
% 9.51/6.37 (((~![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))))))),
% 9.51/6.37 inference(rewrite,[status(thm)],[])).
% 9.51/6.37 tff(217,plain,
% 9.51/6.37 (((~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))))))),
% 9.51/6.37 inference(rewrite,[status(thm)],[])).
% 9.51/6.37 tff(218,plain,
% 9.51/6.37 (((~![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)))))))),
% 9.51/6.37 inference(monotonicity,[status(thm)],[217])).
% 9.51/6.37 tff(219,plain,
% 9.51/6.37 (((~![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))))))),
% 9.51/6.37 inference(transitivity,[status(thm)],[218, 216])).
% 9.51/6.37 tff(220,plain,
% 9.51/6.37 ((~![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))))))),
% 9.51/6.37 inference(quant_inst,[status(thm)],[])).
% 9.51/6.37 tff(221,plain,
% 9.51/6.37 ((~![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)))))),
% 9.51/6.37 inference(modus_ponens,[status(thm)],[220, 219])).
% 9.51/6.37 tff(222,plain,
% 9.51/6.37 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 9.51/6.37 inference(unit_resolution,[status(thm)],[221, 215, 35])).
% 9.51/6.37 tff(223,plain,
% 9.51/6.37 (((~![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))))),
% 9.51/6.37 inference(rewrite,[status(thm)],[])).
% 9.51/6.37 tff(224,plain,
% 9.51/6.37 (((~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))))),
% 9.51/6.37 inference(rewrite,[status(thm)],[])).
% 9.51/6.37 tff(225,plain,
% 9.51/6.37 (((~![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)))))),
% 9.51/6.37 inference(monotonicity,[status(thm)],[224])).
% 9.51/6.37 tff(226,plain,
% 9.51/6.37 (((~![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))))),
% 9.51/6.40 inference(transitivity,[status(thm)],[225, 223])).
% 9.51/6.40 tff(227,plain,
% 9.51/6.40 ((~![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)))))),
% 9.51/6.40 inference(quant_inst,[status(thm)],[])).
% 9.51/6.40 tff(228,plain,
% 9.51/6.40 ((~![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)))),
% 9.51/6.40 inference(modus_ponens,[status(thm)],[227, 226])).
% 9.51/6.40 tff(229,plain,
% 9.51/6.40 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 9.51/6.40 inference(unit_resolution,[status(thm)],[228, 35, 222])).
% 9.51/6.40 tff(230,plain,
% 9.51/6.40 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, 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(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49)))),
% 9.51/6.40 inference(rewrite,[status(thm)],[])).
% 9.51/6.40 tff(231,plain,
% 9.51/6.40 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49)))),
% 9.51/6.40 inference(quant_inst,[status(thm)],[])).
% 9.51/6.40 tff(232,plain,
% 9.51/6.40 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))),
% 9.51/6.40 inference(modus_ponens,[status(thm)],[231, 230])).
% 9.51/6.40 tff(233,plain,
% 9.51/6.40 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))),
% 9.51/6.40 inference(unit_resolution,[status(thm)],[232, 92, 229])).
% 9.51/6.40 tff(234,plain,
% 9.51/6.40 (ssList(Z!51)),
% 9.51/6.40 inference(and_elim,[status(thm)],[31])).
% 9.51/6.40 tff(235,plain,
% 9.51/6.40 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | ((~ssList(Z!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Z!51), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | (~ssList(Z!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Z!51), W!49))),
% 9.51/6.40 inference(rewrite,[status(thm)],[])).
% 9.51/6.40 tff(236,plain,
% 9.51/6.40 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | ((~ssList(Z!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Z!51), W!49))),
% 9.51/6.40 inference(quant_inst,[status(thm)],[])).
% 9.51/6.40 tff(237,plain,
% 9.51/6.40 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | (~ssList(Z!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Z!51), W!49)),
% 9.51/6.40 inference(modus_ponens,[status(thm)],[236, 235])).
% 9.51/6.40 tff(238,plain,
% 9.51/6.40 (segmentP(app(app(nil, W!49), Z!51), W!49)),
% 9.51/6.40 inference(unit_resolution,[status(thm)],[237, 234, 71, 233])).
% 9.51/6.40 tff(239,plain,
% 9.51/6.40 ($false),
% 9.51/6.40 inference(unit_resolution,[status(thm)],[238, 202])).
% 9.51/6.40 % SZS output end Proof
%------------------------------------------------------------------------------