TSTP Solution File: SWC104+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC104+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 11:55:17 EDT 2022
% Result : Theorem 6.35s 4.33s
% Output : Proof 6.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC104+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 21:25:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 6.35/4.33 % SZS status Theorem
% 6.35/4.33 % SZS output start Proof
% 6.35/4.33 tff(neq_type, type, (
% 6.35/4.33 neq: ( $i * $i ) > $o)).
% 6.35/4.33 tff(nil_type, type, (
% 6.35/4.33 nil: $i)).
% 6.35/4.33 tff(tptp_fun_U_47_type, type, (
% 6.35/4.33 tptp_fun_U_47: $i)).
% 6.35/4.33 tff(tptp_fun_W_49_type, type, (
% 6.35/4.33 tptp_fun_W_49: $i)).
% 6.35/4.33 tff(leq_type, type, (
% 6.35/4.33 leq: ( $i * $i ) > $o)).
% 6.35/4.33 tff(app_type, type, (
% 6.35/4.33 app: ( $i * $i ) > $i)).
% 6.35/4.33 tff(cons_type, type, (
% 6.35/4.33 cons: ( $i * $i ) > $i)).
% 6.35/4.33 tff(ssList_type, type, (
% 6.35/4.33 ssList: $i > $o)).
% 6.35/4.33 tff(ssItem_type, type, (
% 6.35/4.33 ssItem: $i > $o)).
% 6.35/4.33 tff(tptp_fun_Y_51_type, type, (
% 6.35/4.33 tptp_fun_Y_51: $i)).
% 6.35/4.33 tff(tptp_fun_X_50_type, type, (
% 6.35/4.33 tptp_fun_X_50: $i)).
% 6.35/4.33 tff(totalorderedP_type, type, (
% 6.35/4.33 totalorderedP: $i > $o)).
% 6.35/4.33 tff(tptp_fun_V_48_type, type, (
% 6.35/4.33 tptp_fun_V_48: $i)).
% 6.35/4.33 tff(frontsegP_type, type, (
% 6.35/4.33 frontsegP: ( $i * $i ) > $o)).
% 6.35/4.33 tff(segmentP_type, type, (
% 6.35/4.33 segmentP: ( $i * $i ) > $o)).
% 6.35/4.33 tff(1,plain,
% 6.35/4.33 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(2,plain,
% 6.35/4.33 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(3,plain,
% 6.35/4.33 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(4,plain,
% 6.35/4.33 (((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & (totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(5,plain,
% 6.35/4.33 (((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))) <=> (totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(6,plain,
% 6.35/4.33 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(7,plain,
% 6.35/4.33 ((~(~neq(V!48, nil))) <=> neq(V!48, nil)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(8,plain,
% 6.35/4.33 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(9,plain,
% 6.35/4.33 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(10,plain,
% 6.35/4.33 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & (totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))),
% 6.35/4.33 inference(monotonicity,[status(thm)],[9, 8, 7, 6, 5])).
% 6.35/4.33 tff(11,plain,
% 6.35/4.33 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(transitivity,[status(thm)],[10, 4])).
% 6.35/4.33 tff(12,plain,
% 6.35/4.33 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(13,plain,
% 6.35/4.33 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))),
% 6.35/4.33 inference(monotonicity,[status(thm)],[12, 11])).
% 6.35/4.33 tff(14,plain,
% 6.35/4.33 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(transitivity,[status(thm)],[13, 3])).
% 6.35/4.33 tff(15,plain,
% 6.35/4.33 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(16,plain,
% 6.35/4.33 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))),
% 6.35/4.33 inference(monotonicity,[status(thm)],[15, 14])).
% 6.35/4.33 tff(17,plain,
% 6.35/4.33 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.33 inference(transitivity,[status(thm)],[16, 2])).
% 6.35/4.33 tff(18,plain,
% 6.35/4.33 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 6.35/4.33 inference(rewrite,[status(thm)],[])).
% 6.35/4.33 tff(19,plain,
% 6.35/4.33 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))),
% 6.35/4.34 inference(monotonicity,[status(thm)],[18, 17])).
% 6.35/4.34 tff(20,plain,
% 6.35/4.34 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ((~(~totalorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z)))))))),
% 6.35/4.34 inference(transitivity,[status(thm)],[19, 1])).
% 6.35/4.34 tff(21,plain,
% 6.35/4.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z)))))))))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(22,plain,
% 6.35/4.34 ((~![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) => (((~(app(W, Y) = X)) | (~totalorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & leq(X2, Z)))))))) | ((~(nil = X)) & (nil = W))) | (neq(U, nil) & frontsegP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z)))))))))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 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) => (((~(app(W, Y) = X)) | (~totalorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & leq(X2, Z)))))))) | ((~(nil = X)) & (nil = W))) | (neq(U, nil) & frontsegP(V, U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 6.35/4.34 tff(24,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[23, 22])).
% 6.35/4.34 tff(25,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[24, 21])).
% 6.35/4.34 tff(26,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[25, 21])).
% 6.35/4.34 tff(27,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[26, 21])).
% 6.35/4.34 tff(28,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[27, 21])).
% 6.35/4.34 tff(29,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[28, 21])).
% 6.35/4.34 tff(30,plain,
% 6.35/4.34 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (neq(U, nil) & frontsegP(V, U)) | (~neq(V, nil)) | (~ssList(X)) | ![Y: $i] : ((~totalorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & leq(X2, Z))))))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[29, 21])).
% 6.35/4.34 tff(31,plain,
% 6.35/4.34 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (~(neq(U!47, nil) & frontsegP(V!48, U!47))) & neq(V!48, nil) & ssList(X!50) & totalorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & leq(X2, Z))))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[30, 20])).
% 6.35/4.34 tff(32,plain,
% 6.35/4.34 (U!47 = W!49),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(33,plain,
% 6.35/4.34 (W!49 = U!47),
% 6.35/4.34 inference(symmetry,[status(thm)],[32])).
% 6.35/4.34 tff(34,plain,
% 6.35/4.34 (neq(W!49, nil) <=> neq(U!47, nil)),
% 6.35/4.34 inference(monotonicity,[status(thm)],[33])).
% 6.35/4.34 tff(35,plain,
% 6.35/4.34 (ssList(W!49)),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(36,plain,
% 6.35/4.34 (^[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))))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(37,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[36])).
% 6.35/4.34 tff(38,plain,
% 6.35/4.34 (^[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))))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(39,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[38])).
% 6.35/4.34 tff(40,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(transitivity,[status(thm)],[39, 37])).
% 6.35/4.34 tff(41,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(42,plain,
% 6.35/4.34 (^[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)))))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(43,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[42])).
% 6.35/4.34 tff(44,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 6.35/4.34 tff(45,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[44, 43])).
% 6.35/4.34 tff(46,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[45, 41])).
% 6.35/4.34 tff(47,plain,(
% 6.35/4.34 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 6.35/4.34 inference(skolemize,[status(sab)],[46])).
% 6.35/4.34 tff(48,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[47, 40])).
% 6.35/4.34 tff(49,plain,
% 6.35/4.34 (((~![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)))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(50,plain,
% 6.35/4.34 ((~![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)))))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(51,plain,
% 6.35/4.34 ((~![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))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[50, 49])).
% 6.35/4.34 tff(52,plain,
% 6.35/4.34 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[51, 48, 35])).
% 6.35/4.34 tff(53,plain,
% 6.35/4.34 (ssList(nil) <=> ssList(nil)),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(54,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 6.35/4.34 tff(55,plain,
% 6.35/4.34 (ssList(nil)),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[54, 53])).
% 6.35/4.34 tff(56,plain,
% 6.35/4.34 (((~![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))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(57,plain,
% 6.35/4.34 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(58,plain,
% 6.35/4.34 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[57, 56])).
% 6.35/4.34 tff(59,plain,
% 6.35/4.34 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[58, 55, 52])).
% 6.35/4.34 tff(60,plain,
% 6.35/4.34 ((W!49 = nil) <=> (nil = W!49)),
% 6.35/4.34 inference(commutativity,[status(thm)],[])).
% 6.35/4.34 tff(61,plain,
% 6.35/4.34 ((nil = W!49) <=> (W!49 = nil)),
% 6.35/4.34 inference(symmetry,[status(thm)],[60])).
% 6.35/4.34 tff(62,plain,
% 6.35/4.34 ((~(nil = W!49)) <=> (~(W!49 = nil))),
% 6.35/4.34 inference(monotonicity,[status(thm)],[61])).
% 6.35/4.34 tff(63,plain,
% 6.35/4.34 (ssList(X!50)),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(64,plain,
% 6.35/4.34 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(65,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[64])).
% 6.35/4.34 tff(66,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(67,plain,
% 6.35/4.34 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(68,plain,
% 6.35/4.34 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[67])).
% 6.35/4.34 tff(69,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 6.35/4.34 tff(70,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[69, 68])).
% 6.35/4.34 tff(71,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[70, 66])).
% 6.35/4.34 tff(72,plain,(
% 6.35/4.34 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(skolemize,[status(sab)],[71])).
% 6.35/4.34 tff(73,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[72, 65])).
% 6.35/4.34 tff(74,plain,
% 6.35/4.34 (((~![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)))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(75,plain,
% 6.35/4.34 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(76,plain,
% 6.35/4.34 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[75, 74])).
% 6.35/4.34 tff(77,plain,
% 6.35/4.34 (segmentP(nil, X!50) <=> (nil = X!50)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[76, 73, 63])).
% 6.35/4.34 tff(78,plain,
% 6.35/4.34 (((~![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)))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(79,plain,
% 6.35/4.34 ((~![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)))))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(80,plain,
% 6.35/4.34 ((~![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))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[79, 78])).
% 6.35/4.34 tff(81,plain,
% 6.35/4.34 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[80, 48, 63])).
% 6.35/4.34 tff(82,plain,
% 6.35/4.34 (((~![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))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(83,plain,
% 6.35/4.34 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(84,plain,
% 6.35/4.34 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[83, 82])).
% 6.35/4.34 tff(85,plain,
% 6.35/4.34 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[84, 55, 81])).
% 6.35/4.34 tff(86,plain,
% 6.35/4.34 (V!48 = X!50),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(87,plain,
% 6.35/4.34 (X!50 = V!48),
% 6.35/4.34 inference(symmetry,[status(thm)],[86])).
% 6.35/4.34 tff(88,plain,
% 6.35/4.34 (neq(X!50, nil) <=> neq(V!48, nil)),
% 6.35/4.34 inference(monotonicity,[status(thm)],[87])).
% 6.35/4.34 tff(89,plain,
% 6.35/4.34 (neq(V!48, nil) <=> neq(X!50, nil)),
% 6.35/4.34 inference(symmetry,[status(thm)],[88])).
% 6.35/4.34 tff(90,plain,
% 6.35/4.34 (neq(V!48, nil)),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(91,plain,
% 6.35/4.34 (neq(X!50, nil)),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[90, 89])).
% 6.35/4.34 tff(92,plain,
% 6.35/4.34 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 6.35/4.34 inference(tautology,[status(thm)],[])).
% 6.35/4.34 tff(93,plain,
% 6.35/4.34 (~(X!50 = nil)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[92, 91, 85])).
% 6.35/4.34 tff(94,plain,
% 6.35/4.34 (^[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)))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(95,plain,
% 6.35/4.34 (![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))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[94])).
% 6.35/4.34 tff(96,plain,
% 6.35/4.34 (^[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)))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(97,plain,
% 6.35/4.34 (![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))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[96])).
% 6.35/4.34 tff(98,plain,
% 6.35/4.34 (![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))))),
% 6.35/4.34 inference(transitivity,[status(thm)],[97, 95])).
% 6.35/4.34 tff(99,plain,
% 6.35/4.34 (^[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)))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(100,plain,
% 6.35/4.34 (![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))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[99])).
% 6.35/4.34 tff(101,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(102,plain,
% 6.35/4.34 (^[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)))))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(103,plain,
% 6.35/4.34 (![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)))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[102])).
% 6.35/4.34 tff(104,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 6.35/4.34 tff(105,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[104, 103])).
% 6.35/4.34 tff(106,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[105, 101])).
% 6.35/4.34 tff(107,plain,(
% 6.35/4.34 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 6.35/4.34 inference(skolemize,[status(sab)],[106])).
% 6.35/4.34 tff(108,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[107, 100])).
% 6.35/4.34 tff(109,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[108, 98])).
% 6.35/4.34 tff(110,plain,
% 6.35/4.34 (((~![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))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(111,plain,
% 6.35/4.34 (((~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))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(112,plain,
% 6.35/4.34 (((~![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)))))),
% 6.35/4.34 inference(monotonicity,[status(thm)],[111])).
% 6.35/4.34 tff(113,plain,
% 6.35/4.34 (((~![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))))),
% 6.35/4.34 inference(transitivity,[status(thm)],[112, 110])).
% 6.35/4.34 tff(114,plain,
% 6.35/4.34 ((~![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))))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(115,plain,
% 6.35/4.34 ((~![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)))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[114, 113])).
% 6.35/4.34 tff(116,plain,
% 6.35/4.34 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[115, 109, 63])).
% 6.35/4.34 tff(117,plain,
% 6.35/4.34 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(118,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[117])).
% 6.35/4.34 tff(119,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(120,plain,
% 6.35/4.34 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(121,plain,
% 6.35/4.34 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[120])).
% 6.35/4.34 tff(122,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 6.35/4.34 tff(123,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[122, 121])).
% 6.35/4.34 tff(124,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[123, 119])).
% 6.35/4.34 tff(125,plain,(
% 6.35/4.34 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(skolemize,[status(sab)],[124])).
% 6.35/4.34 tff(126,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[125, 118])).
% 6.35/4.34 tff(127,plain,
% 6.35/4.34 (((~![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))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(128,plain,
% 6.35/4.34 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(129,plain,
% 6.35/4.34 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[128, 127])).
% 6.35/4.34 tff(130,plain,
% 6.35/4.34 (segmentP(X!50, nil)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[129, 126, 63])).
% 6.35/4.34 tff(131,plain,
% 6.35/4.34 (((~![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)))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(132,plain,
% 6.35/4.34 (((~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)))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(133,plain,
% 6.35/4.34 (((~![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))))),
% 6.35/4.34 inference(monotonicity,[status(thm)],[132])).
% 6.35/4.34 tff(134,plain,
% 6.35/4.34 (((~![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)))),
% 6.35/4.34 inference(transitivity,[status(thm)],[133, 131])).
% 6.35/4.34 tff(135,plain,
% 6.35/4.34 ((~![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)))),
% 6.35/4.34 inference(quant_inst,[status(thm)],[])).
% 6.35/4.34 tff(136,plain,
% 6.35/4.34 ((~![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))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[135, 134])).
% 6.35/4.34 tff(137,plain,
% 6.35/4.34 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[136, 55, 130, 116])).
% 6.35/4.34 tff(138,plain,
% 6.35/4.34 (~segmentP(nil, X!50)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[137, 93])).
% 6.35/4.34 tff(139,plain,
% 6.35/4.34 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 6.35/4.34 inference(tautology,[status(thm)],[])).
% 6.35/4.34 tff(140,plain,
% 6.35/4.34 (~(nil = X!50)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[139, 138, 77])).
% 6.35/4.34 tff(141,plain,
% 6.35/4.34 ((~(~((nil = X!50) | (~(nil = W!49))))) <=> ((nil = X!50) | (~(nil = W!49)))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(142,plain,
% 6.35/4.34 (((~(nil = X!50)) & (nil = W!49)) <=> (~((nil = X!50) | (~(nil = W!49))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(143,plain,
% 6.35/4.34 ((~((~(nil = X!50)) & (nil = W!49))) <=> (~(~((nil = X!50) | (~(nil = W!49)))))),
% 6.35/4.34 inference(monotonicity,[status(thm)],[142])).
% 6.35/4.34 tff(144,plain,
% 6.35/4.34 ((~((~(nil = X!50)) & (nil = W!49))) <=> ((nil = X!50) | (~(nil = W!49)))),
% 6.35/4.34 inference(transitivity,[status(thm)],[143, 141])).
% 6.35/4.34 tff(145,plain,
% 6.35/4.34 (~((~(nil = X!50)) & (nil = W!49))),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(146,plain,
% 6.35/4.34 ((nil = X!50) | (~(nil = W!49))),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[145, 144])).
% 6.35/4.34 tff(147,plain,
% 6.35/4.34 (~(nil = W!49)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[146, 140])).
% 6.35/4.34 tff(148,plain,
% 6.35/4.34 (~(W!49 = nil)),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[147, 62])).
% 6.35/4.34 tff(149,plain,
% 6.35/4.34 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 6.35/4.34 inference(tautology,[status(thm)],[])).
% 6.35/4.34 tff(150,plain,
% 6.35/4.34 (neq(W!49, nil)),
% 6.35/4.34 inference(unit_resolution,[status(thm)],[149, 148, 59])).
% 6.35/4.34 tff(151,plain,
% 6.35/4.34 (neq(U!47, nil)),
% 6.35/4.34 inference(modus_ponens,[status(thm)],[150, 34])).
% 6.35/4.34 tff(152,plain,
% 6.35/4.34 (app(W!49, Y!51) = X!50),
% 6.35/4.34 inference(and_elim,[status(thm)],[31])).
% 6.35/4.34 tff(153,plain,
% 6.35/4.34 (app(W!49, Y!51) = V!48),
% 6.35/4.34 inference(transitivity,[status(thm)],[152, 87])).
% 6.35/4.34 tff(154,plain,
% 6.35/4.34 (frontsegP(app(W!49, Y!51), W!49) <=> frontsegP(V!48, U!47)),
% 6.35/4.34 inference(monotonicity,[status(thm)],[153, 33])).
% 6.35/4.34 tff(155,plain,
% 6.35/4.34 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(156,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[155])).
% 6.35/4.34 tff(157,plain,
% 6.35/4.34 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 6.35/4.34 inference(bind,[status(th)],[])).
% 6.35/4.34 tff(158,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.34 inference(quant_intro,[status(thm)],[157])).
% 6.35/4.34 tff(159,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.34 inference(transitivity,[status(thm)],[158, 156])).
% 6.35/4.34 tff(160,plain,
% 6.35/4.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.34 inference(rewrite,[status(thm)],[])).
% 6.35/4.34 tff(161,plain,
% 6.35/4.34 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((frontsegP(U, V) => frontsegP(app(U, W), V)) <=> ((~frontsegP(U, V)) | frontsegP(app(U, W), V))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))))), rewrite((ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), (![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> (ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), rewrite((ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))))),
% 6.35/4.35 inference(bind,[status(th)],[])).
% 6.35/4.35 tff(162,plain,
% 6.35/4.35 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.35 inference(quant_intro,[status(thm)],[161])).
% 6.35/4.35 tff(163,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax43')).
% 6.35/4.35 tff(164,plain,
% 6.35/4.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.35 inference(modus_ponens,[status(thm)],[163, 162])).
% 6.35/4.35 tff(165,plain,
% 6.35/4.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.35 inference(modus_ponens,[status(thm)],[164, 160])).
% 6.35/4.35 tff(166,plain,(
% 6.35/4.35 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.35 inference(skolemize,[status(sab)],[165])).
% 6.35/4.35 tff(167,plain,
% 6.35/4.35 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 6.35/4.35 inference(modus_ponens,[status(thm)],[166, 159])).
% 6.35/4.35 tff(168,plain,
% 6.35/4.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))),
% 6.35/4.35 inference(rewrite,[status(thm)],[])).
% 6.35/4.35 tff(169,plain,
% 6.35/4.35 (((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V))))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))),
% 6.35/4.35 inference(rewrite,[status(thm)],[])).
% 6.35/4.35 tff(170,plain,
% 6.35/4.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))))),
% 6.35/4.35 inference(monotonicity,[status(thm)],[169])).
% 6.35/4.35 tff(171,plain,
% 6.35/4.35 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))),
% 6.35/4.35 inference(transitivity,[status(thm)],[170, 168])).
% 6.35/4.35 tff(172,plain,
% 6.35/4.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V)))))),
% 6.35/4.35 inference(quant_inst,[status(thm)],[])).
% 6.35/4.35 tff(173,plain,
% 6.35/4.35 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))),
% 6.35/4.35 inference(modus_ponens,[status(thm)],[172, 171])).
% 6.35/4.35 tff(174,plain,
% 6.35/4.35 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))),
% 6.35/4.35 inference(unit_resolution,[status(thm)],[173, 167, 35])).
% 6.35/4.35 tff(175,plain,
% 6.35/4.35 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))),
% 6.35/4.35 inference(rewrite,[status(thm)],[])).
% 6.35/4.35 tff(176,plain,
% 6.35/4.35 (((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49)))) <=> ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))),
% 6.35/4.35 inference(rewrite,[status(thm)],[])).
% 6.35/4.35 tff(177,plain,
% 6.35/4.35 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))))),
% 6.35/4.35 inference(monotonicity,[status(thm)],[176])).
% 6.35/4.35 tff(178,plain,
% 6.35/4.35 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))),
% 6.35/4.35 inference(transitivity,[status(thm)],[177, 175])).
% 6.35/4.35 tff(179,plain,
% 6.35/4.35 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49))))),
% 6.35/4.35 inference(quant_inst,[status(thm)],[])).
% 6.35/4.35 tff(180,plain,
% 6.35/4.35 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))),
% 6.35/4.35 inference(modus_ponens,[status(thm)],[179, 178])).
% 6.35/4.35 tff(181,plain,
% 6.35/4.35 (![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))),
% 6.35/4.35 inference(unit_resolution,[status(thm)],[180, 35, 174])).
% 6.35/4.35 tff(182,plain,
% 6.35/4.35 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 6.35/4.35 inference(bind,[status(th)],[])).
% 6.35/4.35 tff(183,plain,
% 6.35/4.35 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.35/4.35 inference(quant_intro,[status(thm)],[182])).
% 6.35/4.35 tff(184,plain,
% 6.35/4.35 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.35/4.35 inference(rewrite,[status(thm)],[])).
% 6.35/4.35 tff(185,plain,
% 6.35/4.35 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 6.46/4.36 inference(bind,[status(th)],[])).
% 6.46/4.36 tff(186,plain,
% 6.46/4.36 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.46/4.36 inference(quant_intro,[status(thm)],[185])).
% 6.46/4.36 tff(187,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax42')).
% 6.46/4.36 tff(188,plain,
% 6.46/4.36 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[187, 186])).
% 6.46/4.36 tff(189,plain,
% 6.46/4.36 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[188, 184])).
% 6.46/4.36 tff(190,plain,(
% 6.46/4.36 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.46/4.36 inference(skolemize,[status(sab)],[189])).
% 6.46/4.36 tff(191,plain,
% 6.46/4.36 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[190, 183])).
% 6.46/4.36 tff(192,plain,
% 6.46/4.36 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49))),
% 6.46/4.36 inference(rewrite,[status(thm)],[])).
% 6.46/4.36 tff(193,plain,
% 6.46/4.36 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))),
% 6.46/4.36 inference(quant_inst,[status(thm)],[])).
% 6.46/4.36 tff(194,plain,
% 6.46/4.36 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49)),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[193, 192])).
% 6.46/4.36 tff(195,plain,
% 6.46/4.36 (frontsegP(W!49, W!49)),
% 6.46/4.36 inference(unit_resolution,[status(thm)],[194, 191, 35])).
% 6.46/4.36 tff(196,plain,
% 6.46/4.36 (ssList(Y!51)),
% 6.46/4.36 inference(and_elim,[status(thm)],[31])).
% 6.46/4.36 tff(197,plain,
% 6.46/4.36 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | ((~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | (~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49))),
% 6.46/4.36 inference(rewrite,[status(thm)],[])).
% 6.46/4.36 tff(198,plain,
% 6.46/4.36 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | ((~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49))),
% 6.46/4.36 inference(quant_inst,[status(thm)],[])).
% 6.46/4.36 tff(199,plain,
% 6.46/4.36 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | (~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49)),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[198, 197])).
% 6.46/4.36 tff(200,plain,
% 6.46/4.36 (frontsegP(app(W!49, Y!51), W!49)),
% 6.46/4.36 inference(unit_resolution,[status(thm)],[199, 196, 195, 181])).
% 6.46/4.36 tff(201,plain,
% 6.46/4.36 (frontsegP(V!48, U!47)),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[200, 154])).
% 6.46/4.36 tff(202,plain,
% 6.46/4.36 ((~(~((~neq(U!47, nil)) | (~frontsegP(V!48, U!47))))) <=> ((~neq(U!47, nil)) | (~frontsegP(V!48, U!47)))),
% 6.46/4.36 inference(rewrite,[status(thm)],[])).
% 6.46/4.36 tff(203,plain,
% 6.46/4.36 ((neq(U!47, nil) & frontsegP(V!48, U!47)) <=> (~((~neq(U!47, nil)) | (~frontsegP(V!48, U!47))))),
% 6.46/4.36 inference(rewrite,[status(thm)],[])).
% 6.46/4.36 tff(204,plain,
% 6.46/4.36 ((~(neq(U!47, nil) & frontsegP(V!48, U!47))) <=> (~(~((~neq(U!47, nil)) | (~frontsegP(V!48, U!47)))))),
% 6.46/4.36 inference(monotonicity,[status(thm)],[203])).
% 6.46/4.36 tff(205,plain,
% 6.46/4.36 ((~(neq(U!47, nil) & frontsegP(V!48, U!47))) <=> ((~neq(U!47, nil)) | (~frontsegP(V!48, U!47)))),
% 6.46/4.36 inference(transitivity,[status(thm)],[204, 202])).
% 6.46/4.36 tff(206,plain,
% 6.46/4.36 (~(neq(U!47, nil) & frontsegP(V!48, U!47))),
% 6.46/4.36 inference(and_elim,[status(thm)],[31])).
% 6.46/4.36 tff(207,plain,
% 6.46/4.36 ((~neq(U!47, nil)) | (~frontsegP(V!48, U!47))),
% 6.46/4.36 inference(modus_ponens,[status(thm)],[206, 205])).
% 6.46/4.36 tff(208,plain,
% 6.46/4.36 (~neq(U!47, nil)),
% 6.46/4.36 inference(unit_resolution,[status(thm)],[207, 201])).
% 6.46/4.36 tff(209,plain,
% 6.46/4.36 ($false),
% 6.46/4.36 inference(unit_resolution,[status(thm)],[208, 151])).
% 6.46/4.36 % SZS output end Proof
%------------------------------------------------------------------------------