TSTP Solution File: SWC331+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC331+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:57:09 EDT 2022
% Result : Theorem 6.51s 4.42s
% Output : Proof 6.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC331+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 00:13:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 6.51/4.42 % SZS status Theorem
% 6.51/4.42 % SZS output start Proof
% 6.51/4.42 tff(segmentP_type, type, (
% 6.51/4.42 segmentP: ( $i * $i ) > $o)).
% 6.51/4.42 tff(tptp_fun_W_49_type, type, (
% 6.51/4.42 tptp_fun_W_49: $i)).
% 6.51/4.42 tff(app_type, type, (
% 6.51/4.42 app: ( $i * $i ) > $i)).
% 6.51/4.42 tff(tptp_fun_Y_51_type, type, (
% 6.51/4.42 tptp_fun_Y_51: $i)).
% 6.51/4.42 tff(tptp_fun_W_6_type, type, (
% 6.51/4.42 tptp_fun_W_6: ( $i * $i ) > $i)).
% 6.51/4.42 tff(tptp_fun_U_47_type, type, (
% 6.51/4.42 tptp_fun_U_47: $i)).
% 6.51/4.42 tff(tptp_fun_V_48_type, type, (
% 6.51/4.42 tptp_fun_V_48: $i)).
% 6.51/4.42 tff(cons_type, type, (
% 6.51/4.42 cons: ( $i * $i ) > $i)).
% 6.51/4.42 tff(nil_type, type, (
% 6.51/4.42 nil: $i)).
% 6.51/4.42 tff(ssList_type, type, (
% 6.51/4.42 ssList: $i > $o)).
% 6.51/4.42 tff(ssItem_type, type, (
% 6.51/4.42 ssItem: $i > $o)).
% 6.51/4.42 tff(equalelemsP_type, type, (
% 6.51/4.42 equalelemsP: $i > $o)).
% 6.51/4.42 tff(tptp_fun_X_50_type, type, (
% 6.51/4.42 tptp_fun_X_50: $i)).
% 6.51/4.42 tff(rearsegP_type, type, (
% 6.51/4.42 rearsegP: ( $i * $i ) > $o)).
% 6.51/4.42 tff(1,plain,
% 6.51/4.42 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(2,plain,
% 6.51/4.42 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(3,plain,
% 6.51/4.42 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(4,plain,
% 6.51/4.42 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(5,plain,
% 6.51/4.42 (((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) <=> ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(6,plain,
% 6.51/4.42 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(7,plain,
% 6.51/4.42 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(8,plain,
% 6.51/4.42 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(9,plain,
% 6.51/4.42 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 6.51/4.42 inference(monotonicity,[status(thm)],[8, 7, 6, 5])).
% 6.51/4.42 tff(10,plain,
% 6.51/4.42 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(transitivity,[status(thm)],[9, 4])).
% 6.51/4.42 tff(11,plain,
% 6.51/4.42 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(12,plain,
% 6.51/4.42 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 6.51/4.42 inference(monotonicity,[status(thm)],[11, 10])).
% 6.51/4.42 tff(13,plain,
% 6.51/4.42 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(transitivity,[status(thm)],[12, 3])).
% 6.51/4.42 tff(14,plain,
% 6.51/4.42 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(15,plain,
% 6.51/4.42 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 6.51/4.42 inference(monotonicity,[status(thm)],[14, 13])).
% 6.51/4.42 tff(16,plain,
% 6.51/4.42 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(transitivity,[status(thm)],[15, 2])).
% 6.51/4.42 tff(17,plain,
% 6.51/4.42 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(18,plain,
% 6.51/4.42 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 6.51/4.42 inference(monotonicity,[status(thm)],[17, 16])).
% 6.51/4.42 tff(19,plain,
% 6.51/4.42 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 6.51/4.42 inference(transitivity,[status(thm)],[18, 1])).
% 6.51/4.42 tff(20,plain,
% 6.51/4.42 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(21,plain,
% 6.51/4.42 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & equalelemsP(U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(22,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & equalelemsP(U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 6.51/4.42 tff(23,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 6.51/4.42 tff(24,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[23, 20])).
% 6.51/4.42 tff(25,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 6.51/4.42 tff(26,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[25, 20])).
% 6.51/4.42 tff(27,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[26, 20])).
% 6.51/4.42 tff(28,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[27, 20])).
% 6.51/4.42 tff(29,plain,
% 6.51/4.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & equalelemsP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[28, 20])).
% 6.51/4.42 tff(30,plain,
% 6.51/4.42 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & equalelemsP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[29, 19])).
% 6.51/4.42 tff(31,plain,
% 6.51/4.42 (U!47 = W!49),
% 6.51/4.42 inference(and_elim,[status(thm)],[30])).
% 6.51/4.42 tff(32,plain,
% 6.51/4.42 (W!49 = U!47),
% 6.51/4.42 inference(symmetry,[status(thm)],[31])).
% 6.51/4.42 tff(33,plain,
% 6.51/4.42 (V!48 = X!50),
% 6.51/4.42 inference(and_elim,[status(thm)],[30])).
% 6.51/4.42 tff(34,plain,
% 6.51/4.42 (X!50 = V!48),
% 6.51/4.42 inference(symmetry,[status(thm)],[33])).
% 6.51/4.42 tff(35,plain,
% 6.51/4.42 (app(W!49, Y!51) = X!50),
% 6.51/4.42 inference(and_elim,[status(thm)],[30])).
% 6.51/4.42 tff(36,plain,
% 6.51/4.42 (ssList(W!49)),
% 6.51/4.42 inference(and_elim,[status(thm)],[30])).
% 6.51/4.42 tff(37,plain,
% 6.51/4.42 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 6.51/4.42 inference(bind,[status(th)],[])).
% 6.51/4.42 tff(38,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 6.51/4.42 inference(quant_intro,[status(thm)],[37])).
% 6.51/4.42 tff(39,plain,
% 6.51/4.42 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 6.51/4.42 inference(bind,[status(th)],[])).
% 6.51/4.42 tff(40,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 6.51/4.42 inference(quant_intro,[status(thm)],[39])).
% 6.51/4.42 tff(41,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 6.51/4.42 inference(transitivity,[status(thm)],[40, 38])).
% 6.51/4.42 tff(42,plain,
% 6.51/4.42 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 6.51/4.42 inference(bind,[status(th)],[])).
% 6.51/4.42 tff(43,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 6.51/4.42 inference(quant_intro,[status(thm)],[42])).
% 6.51/4.42 tff(44,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(45,plain,
% 6.51/4.42 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))) <=> (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), rewrite((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), (![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))))),
% 6.51/4.42 inference(bind,[status(th)],[])).
% 6.51/4.42 tff(46,plain,
% 6.51/4.42 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 6.51/4.42 inference(quant_intro,[status(thm)],[45])).
% 6.51/4.42 tff(47,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax6')).
% 6.51/4.42 tff(48,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 6.51/4.42 tff(49,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 6.51/4.42 tff(50,plain,(
% 6.51/4.42 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U)))))))),
% 6.51/4.42 inference(skolemize,[status(sab)],[49])).
% 6.51/4.42 tff(51,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[50, 43])).
% 6.51/4.42 tff(52,plain,
% 6.51/4.42 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[51, 41])).
% 6.51/4.42 tff(53,plain,
% 6.51/4.42 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49)))))))))),
% 6.51/4.42 inference(rewrite,[status(thm)],[])).
% 6.51/4.42 tff(54,plain,
% 6.51/4.42 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49)))))))))),
% 6.51/4.42 inference(quant_inst,[status(thm)],[])).
% 6.51/4.42 tff(55,plain,
% 6.51/4.42 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49))))))))),
% 6.51/4.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 6.51/4.42 tff(56,plain,
% 6.51/4.42 (![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49))))))))),
% 6.51/4.42 inference(unit_resolution,[status(thm)],[55, 52, 36])).
% 6.51/4.42 tff(57,plain,
% 6.51/4.42 (((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49))))))))) | ((~ssList(W!49)) | (~((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~(rearsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = W!49))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49))))))))) | (~ssList(W!49)) | (~((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~(rearsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = W!49))))))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(58,plain,
% 6.51/4.43 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49))))))))) | ((~ssList(W!49)) | (~((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~(rearsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = W!49))))))))),
% 6.51/4.43 inference(quant_inst,[status(thm)],[])).
% 6.51/4.43 tff(59,plain,
% 6.51/4.43 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(W!49, V)) | (~((~ssList(tptp_fun_W_6(V, W!49))) | (~(app(tptp_fun_W_6(V, W!49), V) = W!49)))))) | (~(rearsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = W!49))))))))) | (~ssList(W!49)) | (~((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~(rearsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = W!49)))))))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 6.51/4.43 tff(60,plain,
% 6.51/4.43 (~((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~(rearsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = W!49))))))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[59, 36, 56])).
% 6.51/4.43 tff(61,plain,
% 6.51/4.43 (((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~(rearsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = W!49)))))) | ((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))),
% 6.51/4.43 inference(tautology,[status(thm)],[])).
% 6.51/4.43 tff(62,plain,
% 6.51/4.43 ((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49))))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 6.51/4.43 tff(63,plain,
% 6.51/4.43 (^[U: $i] : refl(((~ssList(U)) | rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 6.51/4.43 inference(bind,[status(th)],[])).
% 6.51/4.43 tff(64,plain,
% 6.51/4.43 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(quant_intro,[status(thm)],[63])).
% 6.51/4.43 tff(65,plain,
% 6.51/4.43 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(66,plain,
% 6.51/4.43 (^[U: $i] : rewrite((ssList(U) => rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 6.51/4.43 inference(bind,[status(th)],[])).
% 6.51/4.43 tff(67,plain,
% 6.51/4.43 (![U: $i] : (ssList(U) => rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(quant_intro,[status(thm)],[66])).
% 6.51/4.43 tff(68,axiom,(![U: $i] : (ssList(U) => rearsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax49')).
% 6.51/4.43 tff(69,plain,
% 6.51/4.43 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 6.51/4.43 tff(70,plain,
% 6.51/4.43 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[69, 65])).
% 6.51/4.43 tff(71,plain,(
% 6.51/4.43 ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(skolemize,[status(sab)],[70])).
% 6.51/4.43 tff(72,plain,
% 6.51/4.43 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[71, 64])).
% 6.51/4.43 tff(73,plain,
% 6.51/4.43 (((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(W!49)) | rearsegP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(W!49)) | rearsegP(W!49, W!49))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(74,plain,
% 6.51/4.43 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(W!49)) | rearsegP(W!49, W!49))),
% 6.51/4.43 inference(quant_inst,[status(thm)],[])).
% 6.51/4.43 tff(75,plain,
% 6.51/4.43 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(W!49)) | rearsegP(W!49, W!49)),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 6.51/4.43 tff(76,plain,
% 6.51/4.43 (rearsegP(W!49, W!49)),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[75, 72, 36])).
% 6.51/4.43 tff(77,plain,
% 6.51/4.43 ((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49))))),
% 6.51/4.43 inference(tautology,[status(thm)],[])).
% 6.51/4.43 tff(78,plain,
% 6.51/4.43 ((~((~rearsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))))) | (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49))))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[77, 76])).
% 6.51/4.43 tff(79,plain,
% 6.51/4.43 (~((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[78, 62])).
% 6.51/4.43 tff(80,plain,
% 6.51/4.43 (((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49))) | (app(tptp_fun_W_6(W!49, W!49), W!49) = W!49)),
% 6.51/4.43 inference(tautology,[status(thm)],[])).
% 6.51/4.43 tff(81,plain,
% 6.51/4.43 (app(tptp_fun_W_6(W!49, W!49), W!49) = W!49),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 6.51/4.43 tff(82,plain,
% 6.51/4.43 (app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51) = app(W!49, Y!51)),
% 6.51/4.43 inference(monotonicity,[status(thm)],[81])).
% 6.51/4.43 tff(83,plain,
% 6.51/4.43 (app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51) = V!48),
% 6.51/4.43 inference(transitivity,[status(thm)],[82, 35, 34])).
% 6.51/4.43 tff(84,plain,
% 6.51/4.43 (segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49) <=> segmentP(V!48, U!47)),
% 6.51/4.43 inference(monotonicity,[status(thm)],[83, 32])).
% 6.51/4.43 tff(85,plain,
% 6.51/4.43 (segmentP(V!48, U!47) <=> segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49)),
% 6.51/4.43 inference(symmetry,[status(thm)],[84])).
% 6.51/4.43 tff(86,plain,
% 6.51/4.43 ((~segmentP(V!48, U!47)) <=> (~segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49))),
% 6.51/4.43 inference(monotonicity,[status(thm)],[85])).
% 6.51/4.43 tff(87,plain,
% 6.51/4.43 (equalelemsP(U!47) <=> equalelemsP(W!49)),
% 6.51/4.43 inference(monotonicity,[status(thm)],[31])).
% 6.51/4.43 tff(88,plain,
% 6.51/4.43 (equalelemsP(W!49) <=> equalelemsP(U!47)),
% 6.51/4.43 inference(symmetry,[status(thm)],[87])).
% 6.51/4.43 tff(89,plain,
% 6.51/4.43 (equalelemsP(W!49)),
% 6.51/4.43 inference(and_elim,[status(thm)],[30])).
% 6.51/4.43 tff(90,plain,
% 6.51/4.43 (equalelemsP(U!47)),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 6.51/4.43 tff(91,plain,
% 6.51/4.43 ((~(~((~segmentP(V!48, U!47)) | (~equalelemsP(U!47))))) <=> ((~segmentP(V!48, U!47)) | (~equalelemsP(U!47)))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(92,plain,
% 6.51/4.43 ((segmentP(V!48, U!47) & equalelemsP(U!47)) <=> (~((~segmentP(V!48, U!47)) | (~equalelemsP(U!47))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(93,plain,
% 6.51/4.43 ((~(segmentP(V!48, U!47) & equalelemsP(U!47))) <=> (~(~((~segmentP(V!48, U!47)) | (~equalelemsP(U!47)))))),
% 6.51/4.43 inference(monotonicity,[status(thm)],[92])).
% 6.51/4.43 tff(94,plain,
% 6.51/4.43 ((~(segmentP(V!48, U!47) & equalelemsP(U!47))) <=> ((~segmentP(V!48, U!47)) | (~equalelemsP(U!47)))),
% 6.51/4.43 inference(transitivity,[status(thm)],[93, 91])).
% 6.51/4.43 tff(95,plain,
% 6.51/4.43 (~(segmentP(V!48, U!47) & equalelemsP(U!47))),
% 6.51/4.43 inference(and_elim,[status(thm)],[30])).
% 6.51/4.43 tff(96,plain,
% 6.51/4.43 ((~segmentP(V!48, U!47)) | (~equalelemsP(U!47))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 6.51/4.43 tff(97,plain,
% 6.51/4.43 (~segmentP(V!48, U!47)),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[96, 90])).
% 6.51/4.43 tff(98,plain,
% 6.51/4.43 (~segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49)),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[97, 86])).
% 6.51/4.43 tff(99,plain,
% 6.51/4.43 (((~ssList(tptp_fun_W_6(W!49, W!49))) | (~(app(tptp_fun_W_6(W!49, W!49), W!49) = W!49))) | ssList(tptp_fun_W_6(W!49, W!49))),
% 6.51/4.43 inference(tautology,[status(thm)],[])).
% 6.51/4.43 tff(100,plain,
% 6.51/4.43 (ssList(tptp_fun_W_6(W!49, W!49))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[99, 79])).
% 6.51/4.43 tff(101,plain,
% 6.51/4.43 (^[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)))))))),
% 6.51/4.43 inference(bind,[status(th)],[])).
% 6.51/4.43 tff(102,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(quant_intro,[status(thm)],[101])).
% 6.51/4.43 tff(103,plain,
% 6.51/4.43 (^[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)))))))),
% 6.51/4.43 inference(bind,[status(th)],[])).
% 6.51/4.43 tff(104,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(quant_intro,[status(thm)],[103])).
% 6.51/4.43 tff(105,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(transitivity,[status(thm)],[104, 102])).
% 6.51/4.43 tff(106,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(107,plain,
% 6.51/4.43 (^[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))))))))),
% 6.51/4.43 inference(bind,[status(th)],[])).
% 6.51/4.43 tff(108,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(quant_intro,[status(thm)],[107])).
% 6.51/4.43 tff(109,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/sandbox/benchmark/Axioms/SWC001+0.ax','ax56')).
% 6.51/4.43 tff(110,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 6.51/4.43 tff(111,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[110, 106])).
% 6.51/4.43 tff(112,plain,(
% 6.51/4.43 ![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))))))),
% 6.51/4.43 inference(skolemize,[status(sab)],[111])).
% 6.51/4.43 tff(113,plain,
% 6.51/4.43 (![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))))))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[112, 105])).
% 6.51/4.43 tff(114,plain,
% 6.51/4.43 (((~![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))))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(115,plain,
% 6.51/4.43 (((~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))))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(116,plain,
% 6.51/4.43 (((~![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)))))))),
% 6.51/4.43 inference(monotonicity,[status(thm)],[115])).
% 6.51/4.43 tff(117,plain,
% 6.51/4.43 (((~![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))))))),
% 6.51/4.43 inference(transitivity,[status(thm)],[116, 114])).
% 6.51/4.43 tff(118,plain,
% 6.51/4.43 ((~![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))))))),
% 6.51/4.43 inference(quant_inst,[status(thm)],[])).
% 6.51/4.43 tff(119,plain,
% 6.51/4.43 ((~![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)))))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 6.51/4.43 tff(120,plain,
% 6.51/4.43 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[119, 113, 36])).
% 6.51/4.43 tff(121,plain,
% 6.51/4.43 (((~![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))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(122,plain,
% 6.51/4.43 (((~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))))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(123,plain,
% 6.51/4.43 (((~![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)))))),
% 6.51/4.43 inference(monotonicity,[status(thm)],[122])).
% 6.51/4.43 tff(124,plain,
% 6.51/4.43 (((~![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))))),
% 6.51/4.43 inference(transitivity,[status(thm)],[123, 121])).
% 6.51/4.43 tff(125,plain,
% 6.51/4.43 ((~![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)))))),
% 6.51/4.43 inference(quant_inst,[status(thm)],[])).
% 6.51/4.43 tff(126,plain,
% 6.51/4.43 ((~![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)))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 6.51/4.43 tff(127,plain,
% 6.51/4.43 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[126, 36, 120])).
% 6.51/4.43 tff(128,plain,
% 6.51/4.43 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(tptp_fun_W_6(W!49, W!49))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), 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(tptp_fun_W_6(W!49, W!49))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49)))),
% 6.51/4.43 inference(rewrite,[status(thm)],[])).
% 6.51/4.43 tff(129,plain,
% 6.51/4.43 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(tptp_fun_W_6(W!49, W!49))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49)))),
% 6.51/4.43 inference(quant_inst,[status(thm)],[])).
% 6.51/4.43 tff(130,plain,
% 6.51/4.43 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(tptp_fun_W_6(W!49, W!49))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49))),
% 6.51/4.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 6.51/4.43 tff(131,plain,
% 6.51/4.43 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49))),
% 6.51/4.43 inference(unit_resolution,[status(thm)],[130, 127, 100])).
% 6.51/4.43 tff(132,plain,
% 6.51/4.43 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 6.57/4.46 inference(bind,[status(th)],[])).
% 6.57/4.46 tff(133,plain,
% 6.57/4.46 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(quant_intro,[status(thm)],[132])).
% 6.57/4.46 tff(134,plain,
% 6.57/4.46 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(rewrite,[status(thm)],[])).
% 6.57/4.46 tff(135,plain,
% 6.57/4.46 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 6.57/4.46 inference(bind,[status(th)],[])).
% 6.57/4.46 tff(136,plain,
% 6.57/4.46 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(quant_intro,[status(thm)],[135])).
% 6.57/4.46 tff(137,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax55')).
% 6.57/4.46 tff(138,plain,
% 6.57/4.46 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 6.57/4.46 tff(139,plain,
% 6.57/4.46 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(modus_ponens,[status(thm)],[138, 134])).
% 6.57/4.46 tff(140,plain,(
% 6.57/4.46 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(skolemize,[status(sab)],[139])).
% 6.57/4.46 tff(141,plain,
% 6.57/4.46 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 6.57/4.46 inference(modus_ponens,[status(thm)],[140, 133])).
% 6.57/4.46 tff(142,plain,
% 6.57/4.46 (((~![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))),
% 6.57/4.46 inference(rewrite,[status(thm)],[])).
% 6.57/4.46 tff(143,plain,
% 6.57/4.46 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 6.57/4.46 inference(quant_inst,[status(thm)],[])).
% 6.57/4.46 tff(144,plain,
% 6.57/4.46 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 6.57/4.46 inference(modus_ponens,[status(thm)],[143, 142])).
% 6.57/4.46 tff(145,plain,
% 6.57/4.46 (segmentP(W!49, W!49)),
% 6.57/4.46 inference(unit_resolution,[status(thm)],[144, 141, 36])).
% 6.57/4.46 tff(146,plain,
% 6.57/4.46 (ssList(Y!51)),
% 6.57/4.46 inference(and_elim,[status(thm)],[30])).
% 6.57/4.46 tff(147,plain,
% 6.57/4.46 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49))) | ((~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49))) | (~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49))),
% 6.57/4.46 inference(rewrite,[status(thm)],[])).
% 6.57/4.46 tff(148,plain,
% 6.57/4.46 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49))) | ((~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49))),
% 6.57/4.46 inference(quant_inst,[status(thm)],[])).
% 6.57/4.46 tff(149,plain,
% 6.57/4.46 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), X), W!49))) | (~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49)),
% 6.57/4.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 6.57/4.46 tff(150,plain,
% 6.57/4.46 (segmentP(app(app(tptp_fun_W_6(W!49, W!49), W!49), Y!51), W!49)),
% 6.57/4.46 inference(unit_resolution,[status(thm)],[149, 146, 145, 131])).
% 6.57/4.46 tff(151,plain,
% 6.57/4.46 ($false),
% 6.57/4.46 inference(unit_resolution,[status(thm)],[150, 98])).
% 6.57/4.46 % SZS output end Proof
%------------------------------------------------------------------------------