TSTP Solution File: SWC347+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC347+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 11:57:16 EDT 2022
% Result : Theorem 11.03s 7.12s
% Output : Proof 11.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC347+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Sep 4 00:09:27 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 11.03/7.12 % SZS status Theorem
% 11.03/7.12 % SZS output start Proof
% 11.03/7.12 tff(segmentP_type, type, (
% 11.03/7.12 segmentP: ( $i * $i ) > $o)).
% 11.03/7.12 tff(tptp_fun_W_49_type, type, (
% 11.03/7.12 tptp_fun_W_49: $i)).
% 11.03/7.12 tff(app_type, type, (
% 11.03/7.12 app: ( $i * $i ) > $i)).
% 11.03/7.12 tff(tptp_fun_Y_51_type, type, (
% 11.03/7.12 tptp_fun_Y_51: $i)).
% 11.03/7.12 tff(tptp_fun_W_6_type, type, (
% 11.03/7.12 tptp_fun_W_6: ( $i * $i ) > $i)).
% 11.03/7.12 tff(nil_type, type, (
% 11.03/7.12 nil: $i)).
% 11.03/7.12 tff(tptp_fun_U_47_type, type, (
% 11.03/7.12 tptp_fun_U_47: $i)).
% 11.03/7.12 tff(tptp_fun_V_48_type, type, (
% 11.03/7.12 tptp_fun_V_48: $i)).
% 11.03/7.12 tff(lt_type, type, (
% 11.03/7.12 lt: ( $i * $i ) > $o)).
% 11.03/7.12 tff(cons_type, type, (
% 11.03/7.12 cons: ( $i * $i ) > $i)).
% 11.03/7.12 tff(ssList_type, type, (
% 11.03/7.12 ssList: $i > $o)).
% 11.03/7.12 tff(ssItem_type, type, (
% 11.03/7.12 ssItem: $i > $o)).
% 11.03/7.12 tff(tptp_fun_X_50_type, type, (
% 11.03/7.12 tptp_fun_X_50: $i)).
% 11.03/7.12 tff(strictorderedP_type, type, (
% 11.03/7.12 strictorderedP: $i > $o)).
% 11.03/7.12 tff(rearsegP_type, type, (
% 11.03/7.12 rearsegP: ( $i * $i ) > $o)).
% 11.03/7.12 tff(1,plain,
% 11.03/7.12 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(2,plain,
% 11.03/7.12 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(3,plain,
% 11.03/7.12 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(4,plain,
% 11.03/7.12 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (strictorderedP(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) & lt(X2, Z)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(5,plain,
% 11.03/7.12 (((~(~strictorderedP(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) & lt(X2, Z))))))) <=> (strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(6,plain,
% 11.03/7.12 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(7,plain,
% 11.03/7.12 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(8,plain,
% 11.03/7.12 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(9,plain,
% 11.03/7.12 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (strictorderedP(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) & lt(X2, Z))))))))),
% 11.03/7.12 inference(monotonicity,[status(thm)],[8, 7, 6, 5])).
% 11.03/7.12 tff(10,plain,
% 11.03/7.12 (((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(transitivity,[status(thm)],[9, 4])).
% 11.03/7.12 tff(11,plain,
% 11.03/7.12 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(12,plain,
% 11.03/7.12 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z))))))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z))))))))),
% 11.03/7.12 inference(monotonicity,[status(thm)],[11, 10])).
% 11.03/7.12 tff(13,plain,
% 11.03/7.12 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z))))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(transitivity,[status(thm)],[12, 3])).
% 11.03/7.12 tff(14,plain,
% 11.03/7.12 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(15,plain,
% 11.03/7.12 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z))))))))),
% 11.03/7.12 inference(monotonicity,[status(thm)],[14, 13])).
% 11.03/7.12 tff(16,plain,
% 11.03/7.12 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z)))))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.12 inference(transitivity,[status(thm)],[15, 2])).
% 11.03/7.12 tff(17,plain,
% 11.03/7.12 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 11.03/7.12 inference(rewrite,[status(thm)],[])).
% 11.03/7.12 tff(18,plain,
% 11.03/7.12 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z))))))))),
% 11.03/7.13 inference(monotonicity,[status(thm)],[17, 16])).
% 11.03/7.13 tff(19,plain,
% 11.03/7.13 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~strictorderedP(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) & lt(X2, Z))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z)))))))),
% 11.03/7.13 inference(transitivity,[status(thm)],[18, 1])).
% 11.03/7.13 tff(20,plain,
% 11.03/7.13 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z)))))))))))),
% 11.03/7.13 inference(rewrite,[status(thm)],[])).
% 11.03/7.13 tff(21,plain,
% 11.03/7.13 ((~![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)) | (~strictorderedP(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)) & lt(X2, Z)))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & strictorderedP(U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z)))))))))))),
% 11.03/7.13 inference(rewrite,[status(thm)],[])).
% 11.03/7.13 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)) | (~strictorderedP(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)) & lt(X2, Z)))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & strictorderedP(U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 11.03/7.13 tff(23,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[22, 21])).
% 11.03/7.13 tff(24,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[23, 20])).
% 11.03/7.13 tff(25,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[24, 20])).
% 11.03/7.13 tff(26,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[25, 20])).
% 11.03/7.13 tff(27,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[26, 20])).
% 11.03/7.13 tff(28,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[27, 20])).
% 11.03/7.13 tff(29,plain,
% 11.03/7.13 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (segmentP(V, U) & strictorderedP(U)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(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) & lt(X2, Z))))))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[28, 20])).
% 11.03/7.13 tff(30,plain,
% 11.03/7.13 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (~(segmentP(V!48, U!47) & strictorderedP(U!47))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & strictorderedP(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) & lt(X2, Z))))))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[29, 19])).
% 11.03/7.13 tff(31,plain,
% 11.03/7.13 (U!47 = W!49),
% 11.03/7.13 inference(and_elim,[status(thm)],[30])).
% 11.03/7.13 tff(32,plain,
% 11.03/7.13 (W!49 = U!47),
% 11.03/7.13 inference(symmetry,[status(thm)],[31])).
% 11.03/7.13 tff(33,plain,
% 11.03/7.13 (V!48 = X!50),
% 11.03/7.13 inference(and_elim,[status(thm)],[30])).
% 11.03/7.13 tff(34,plain,
% 11.03/7.13 (X!50 = V!48),
% 11.03/7.13 inference(symmetry,[status(thm)],[33])).
% 11.03/7.13 tff(35,plain,
% 11.03/7.13 (app(W!49, Y!51) = X!50),
% 11.03/7.13 inference(and_elim,[status(thm)],[30])).
% 11.03/7.13 tff(36,plain,
% 11.03/7.13 (ssList(W!49)),
% 11.03/7.13 inference(and_elim,[status(thm)],[30])).
% 11.03/7.13 tff(37,plain,
% 11.03/7.13 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 11.03/7.13 inference(bind,[status(th)],[])).
% 11.03/7.13 tff(38,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(quant_intro,[status(thm)],[37])).
% 11.03/7.13 tff(39,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(rewrite,[status(thm)],[])).
% 11.03/7.13 tff(40,plain,
% 11.03/7.13 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 11.03/7.13 inference(bind,[status(th)],[])).
% 11.03/7.13 tff(41,plain,
% 11.03/7.13 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(quant_intro,[status(thm)],[40])).
% 11.03/7.13 tff(42,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 11.03/7.13 tff(43,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[42, 41])).
% 11.03/7.13 tff(44,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[43, 39])).
% 11.03/7.13 tff(45,plain,(
% 11.03/7.13 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(skolemize,[status(sab)],[44])).
% 11.03/7.13 tff(46,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[45, 38])).
% 11.03/7.13 tff(47,plain,
% 11.03/7.13 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 11.03/7.13 inference(rewrite,[status(thm)],[])).
% 11.03/7.13 tff(48,plain,
% 11.03/7.13 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 11.03/7.13 inference(quant_inst,[status(thm)],[])).
% 11.03/7.13 tff(49,plain,
% 11.03/7.13 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49)),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[48, 47])).
% 11.03/7.13 tff(50,plain,
% 11.03/7.13 (app(nil, W!49) = W!49),
% 11.03/7.13 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 11.03/7.13 tff(51,plain,
% 11.03/7.13 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 11.03/7.13 inference(bind,[status(th)],[])).
% 11.03/7.13 tff(52,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(quant_intro,[status(thm)],[51])).
% 11.03/7.13 tff(53,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(rewrite,[status(thm)],[])).
% 11.03/7.13 tff(54,plain,
% 11.03/7.13 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 11.03/7.13 inference(bind,[status(th)],[])).
% 11.03/7.13 tff(55,plain,
% 11.03/7.13 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(quant_intro,[status(thm)],[54])).
% 11.03/7.13 tff(56,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 11.03/7.13 tff(57,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[56, 55])).
% 11.03/7.13 tff(58,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[57, 53])).
% 11.03/7.13 tff(59,plain,(
% 11.03/7.13 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(skolemize,[status(sab)],[58])).
% 11.03/7.13 tff(60,plain,
% 11.03/7.13 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[59, 52])).
% 11.03/7.13 tff(61,plain,
% 11.03/7.13 (ssList(nil) <=> ssList(nil)),
% 11.03/7.13 inference(rewrite,[status(thm)],[])).
% 11.03/7.13 tff(62,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 11.03/7.13 tff(63,plain,
% 11.03/7.13 (ssList(nil)),
% 11.03/7.13 inference(modus_ponens,[status(thm)],[62, 61])).
% 11.03/7.13 tff(64,plain,
% 11.03/7.13 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(65,plain,
% 11.03/7.14 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))),
% 11.03/7.14 inference(quant_inst,[status(thm)],[])).
% 11.03/7.14 tff(66,plain,
% 11.03/7.14 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil)),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[65, 64])).
% 11.03/7.14 tff(67,plain,
% 11.03/7.14 (app(nil, nil) = nil),
% 11.03/7.14 inference(unit_resolution,[status(thm)],[66, 63, 60])).
% 11.03/7.14 tff(68,plain,
% 11.03/7.14 (nil = app(nil, nil)),
% 11.03/7.14 inference(symmetry,[status(thm)],[67])).
% 11.03/7.14 tff(69,plain,
% 11.03/7.14 (^[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))))))))))),
% 11.03/7.14 inference(bind,[status(th)],[])).
% 11.03/7.14 tff(70,plain,
% 11.03/7.14 (![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)))))))))),
% 11.03/7.14 inference(quant_intro,[status(thm)],[69])).
% 11.03/7.14 tff(71,plain,
% 11.03/7.14 (^[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))))))))))),
% 11.03/7.14 inference(bind,[status(th)],[])).
% 11.03/7.14 tff(72,plain,
% 11.03/7.14 (![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)))))))))),
% 11.03/7.14 inference(quant_intro,[status(thm)],[71])).
% 11.03/7.14 tff(73,plain,
% 11.03/7.14 (![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)))))))))),
% 11.03/7.14 inference(transitivity,[status(thm)],[72, 70])).
% 11.03/7.14 tff(74,plain,
% 11.03/7.14 (^[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))))))))))),
% 11.03/7.14 inference(bind,[status(th)],[])).
% 11.03/7.14 tff(75,plain,
% 11.03/7.14 (![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)))))))))),
% 11.03/7.14 inference(quant_intro,[status(thm)],[74])).
% 11.03/7.14 tff(76,plain,
% 11.03/7.14 (![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)))))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(77,plain,
% 11.03/7.14 (^[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)))))))),
% 11.03/7.14 inference(bind,[status(th)],[])).
% 11.03/7.14 tff(78,plain,
% 11.03/7.14 (![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)))))),
% 11.03/7.14 inference(quant_intro,[status(thm)],[77])).
% 11.03/7.14 tff(79,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')).
% 11.03/7.14 tff(80,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[79, 78])).
% 11.03/7.14 tff(81,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[80, 76])).
% 11.03/7.14 tff(82,plain,(
% 11.03/7.14 ![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)))))))),
% 11.03/7.14 inference(skolemize,[status(sab)],[81])).
% 11.03/7.14 tff(83,plain,
% 11.03/7.14 (![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)))))))))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[82, 75])).
% 11.03/7.14 tff(84,plain,
% 11.03/7.14 (![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)))))))))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[83, 73])).
% 11.03/7.14 tff(85,plain,
% 11.03/7.14 (((~![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(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))) <=> ((~![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(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(86,plain,
% 11.03/7.14 ((~![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(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil)))))))))),
% 11.03/7.14 inference(quant_inst,[status(thm)],[])).
% 11.03/7.14 tff(87,plain,
% 11.03/7.14 ((~![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(nil)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[86, 85])).
% 11.03/7.14 tff(88,plain,
% 11.03/7.14 (![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))),
% 11.03/7.14 inference(unit_resolution,[status(thm)],[87, 84, 63])).
% 11.03/7.14 tff(89,plain,
% 11.03/7.14 (((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))) | ((~ssList(nil)) | (~((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))) | (~ssList(nil)) | (~((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))))))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(90,plain,
% 11.03/7.14 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))) | ((~ssList(nil)) | (~((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))))))),
% 11.03/7.14 inference(quant_inst,[status(thm)],[])).
% 11.03/7.14 tff(91,plain,
% 11.03/7.14 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(nil, V)) | (~((~ssList(tptp_fun_W_6(V, nil))) | (~(app(tptp_fun_W_6(V, nil), V) = nil)))))) | (~(rearsegP(nil, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = nil))))))))) | (~ssList(nil)) | (~((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil)))))))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[90, 89])).
% 11.03/7.14 tff(92,plain,
% 11.03/7.14 (~((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil))))))),
% 11.03/7.14 inference(unit_resolution,[status(thm)],[91, 63, 88])).
% 11.03/7.14 tff(93,plain,
% 11.03/7.14 (((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~(rearsegP(nil, nil) | ![W: $i] : ((~ssList(W)) | (~(app(W, nil) = nil)))))) | ((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))),
% 11.03/7.14 inference(tautology,[status(thm)],[])).
% 11.03/7.14 tff(94,plain,
% 11.03/7.14 ((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 11.03/7.14 inference(unit_resolution,[status(thm)],[93, 92])).
% 11.03/7.14 tff(95,plain,
% 11.03/7.14 (^[U: $i] : refl(((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 11.03/7.14 inference(bind,[status(th)],[])).
% 11.03/7.14 tff(96,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(quant_intro,[status(thm)],[95])).
% 11.03/7.14 tff(97,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(98,plain,
% 11.03/7.14 (^[U: $i] : rewrite((ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 11.03/7.14 inference(bind,[status(th)],[])).
% 11.03/7.14 tff(99,plain,
% 11.03/7.14 (![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(quant_intro,[status(thm)],[98])).
% 11.03/7.14 tff(100,axiom,(![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax52')).
% 11.03/7.14 tff(101,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[100, 99])).
% 11.03/7.14 tff(102,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[101, 97])).
% 11.03/7.14 tff(103,plain,(
% 11.03/7.14 ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(skolemize,[status(sab)],[102])).
% 11.03/7.14 tff(104,plain,
% 11.03/7.14 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[103, 96])).
% 11.03/7.14 tff(105,plain,
% 11.03/7.14 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | rearsegP(nil, nil))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(106,plain,
% 11.03/7.14 (((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil))) <=> ((~ssList(nil)) | rearsegP(nil, nil))),
% 11.03/7.14 inference(rewrite,[status(thm)],[])).
% 11.03/7.14 tff(107,plain,
% 11.03/7.14 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | rearsegP(nil, nil)))),
% 11.03/7.14 inference(monotonicity,[status(thm)],[106])).
% 11.03/7.14 tff(108,plain,
% 11.03/7.14 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil))),
% 11.03/7.14 inference(transitivity,[status(thm)],[107, 105])).
% 11.03/7.14 tff(109,plain,
% 11.03/7.14 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(nil)) | (rearsegP(nil, nil) <=> (nil = nil)))),
% 11.03/7.14 inference(quant_inst,[status(thm)],[])).
% 11.03/7.14 tff(110,plain,
% 11.03/7.14 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(nil)) | rearsegP(nil, nil)),
% 11.03/7.14 inference(modus_ponens,[status(thm)],[109, 108])).
% 11.03/7.14 tff(111,plain,
% 11.03/7.14 (rearsegP(nil, nil)),
% 11.03/7.14 inference(unit_resolution,[status(thm)],[110, 63, 104])).
% 11.03/7.14 tff(112,plain,
% 11.03/7.14 ((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 11.03/7.15 inference(tautology,[status(thm)],[])).
% 11.03/7.15 tff(113,plain,
% 11.03/7.15 ((~((~rearsegP(nil, nil)) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))))) | (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))))),
% 11.03/7.15 inference(unit_resolution,[status(thm)],[112, 111])).
% 11.03/7.15 tff(114,plain,
% 11.03/7.15 (~((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil)))),
% 11.03/7.15 inference(unit_resolution,[status(thm)],[113, 94])).
% 11.03/7.15 tff(115,plain,
% 11.03/7.15 (((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))) | (app(tptp_fun_W_6(nil, nil), nil) = nil)),
% 11.03/7.15 inference(tautology,[status(thm)],[])).
% 11.03/7.15 tff(116,plain,
% 11.03/7.15 (app(tptp_fun_W_6(nil, nil), nil) = nil),
% 11.03/7.15 inference(unit_resolution,[status(thm)],[115, 114])).
% 11.03/7.15 tff(117,plain,
% 11.03/7.15 (app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil)),
% 11.03/7.15 inference(transitivity,[status(thm)],[116, 68])).
% 11.03/7.15 tff(118,plain,
% 11.03/7.15 (((~ssList(tptp_fun_W_6(nil, nil))) | (~(app(tptp_fun_W_6(nil, nil), nil) = nil))) | ssList(tptp_fun_W_6(nil, nil))),
% 11.03/7.15 inference(tautology,[status(thm)],[])).
% 11.03/7.15 tff(119,plain,
% 11.03/7.15 (ssList(tptp_fun_W_6(nil, nil))),
% 11.03/7.15 inference(unit_resolution,[status(thm)],[118, 114])).
% 11.03/7.15 tff(120,plain,
% 11.03/7.15 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 11.03/7.15 inference(bind,[status(th)],[])).
% 11.03/7.15 tff(121,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(quant_intro,[status(thm)],[120])).
% 11.03/7.15 tff(122,plain,
% 11.03/7.15 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 11.03/7.15 inference(bind,[status(th)],[])).
% 11.03/7.15 tff(123,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(quant_intro,[status(thm)],[122])).
% 11.03/7.15 tff(124,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(transitivity,[status(thm)],[123, 121])).
% 11.03/7.15 tff(125,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(rewrite,[status(thm)],[])).
% 11.03/7.15 tff(126,plain,
% 11.03/7.15 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((app(W, V) = app(U, V)) => (W = U)) <=> ((~(app(W, V) = app(U, V))) | (W = U))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> (ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))))), rewrite((ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), (![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> (ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))))),
% 11.03/7.15 inference(bind,[status(th)],[])).
% 11.03/7.15 tff(127,plain,
% 11.03/7.15 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(quant_intro,[status(thm)],[126])).
% 11.03/7.15 tff(128,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax79')).
% 11.03/7.15 tff(129,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(modus_ponens,[status(thm)],[128, 127])).
% 11.03/7.15 tff(130,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(modus_ponens,[status(thm)],[129, 125])).
% 11.03/7.15 tff(131,plain,(
% 11.03/7.15 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(skolemize,[status(sab)],[130])).
% 11.03/7.15 tff(132,plain,
% 11.03/7.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 11.03/7.15 inference(modus_ponens,[status(thm)],[131, 124])).
% 11.03/7.15 tff(133,plain,
% 11.03/7.15 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 11.03/7.15 inference(rewrite,[status(thm)],[])).
% 11.03/7.15 tff(134,plain,
% 11.03/7.15 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V)))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 11.03/7.15 inference(rewrite,[status(thm)],[])).
% 11.03/7.15 tff(135,plain,
% 11.03/7.15 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))))),
% 11.03/7.15 inference(monotonicity,[status(thm)],[134])).
% 11.03/7.15 tff(136,plain,
% 11.03/7.15 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 11.15/7.15 inference(transitivity,[status(thm)],[135, 133])).
% 11.15/7.15 tff(137,plain,
% 11.15/7.15 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))),
% 11.15/7.15 inference(quant_inst,[status(thm)],[])).
% 11.15/7.15 tff(138,plain,
% 11.15/7.15 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 11.15/7.15 inference(modus_ponens,[status(thm)],[137, 136])).
% 11.15/7.15 tff(139,plain,
% 11.15/7.15 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 11.15/7.15 inference(unit_resolution,[status(thm)],[138, 63, 132])).
% 11.15/7.15 tff(140,plain,
% 11.15/7.15 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))),
% 11.15/7.15 inference(rewrite,[status(thm)],[])).
% 11.15/7.15 tff(141,plain,
% 11.15/7.15 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil)))))),
% 11.15/7.15 inference(quant_inst,[status(thm)],[])).
% 11.15/7.15 tff(142,plain,
% 11.15/7.15 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(nil)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))),
% 11.15/7.15 inference(modus_ponens,[status(thm)],[141, 140])).
% 11.15/7.15 tff(143,plain,
% 11.15/7.15 (![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))),
% 11.15/7.15 inference(unit_resolution,[status(thm)],[142, 63, 139])).
% 11.15/7.15 tff(144,plain,
% 11.15/7.15 (((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))) <=> ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | (~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))),
% 11.15/7.15 inference(rewrite,[status(thm)],[])).
% 11.15/7.15 tff(145,plain,
% 11.15/7.15 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | ((~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil))))),
% 11.15/7.15 inference(quant_inst,[status(thm)],[])).
% 11.15/7.15 tff(146,plain,
% 11.15/7.15 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, nil) = app(nil, nil))))) | (~ssList(tptp_fun_W_6(nil, nil))) | (tptp_fun_W_6(nil, nil) = nil) | (~(app(tptp_fun_W_6(nil, nil), nil) = app(nil, nil)))),
% 11.15/7.15 inference(modus_ponens,[status(thm)],[145, 144])).
% 11.15/7.15 tff(147,plain,
% 11.15/7.15 (tptp_fun_W_6(nil, nil) = nil),
% 11.15/7.15 inference(unit_resolution,[status(thm)],[146, 143, 119, 117])).
% 11.15/7.15 tff(148,plain,
% 11.15/7.15 (app(tptp_fun_W_6(nil, nil), W!49) = app(nil, W!49)),
% 11.15/7.15 inference(monotonicity,[status(thm)],[147])).
% 11.15/7.15 tff(149,plain,
% 11.15/7.15 (app(tptp_fun_W_6(nil, nil), W!49) = W!49),
% 11.15/7.15 inference(transitivity,[status(thm)],[148, 50])).
% 11.15/7.15 tff(150,plain,
% 11.15/7.15 (app(app(tptp_fun_W_6(nil, nil), W!49), Y!51) = app(W!49, Y!51)),
% 11.15/7.15 inference(monotonicity,[status(thm)],[149])).
% 11.15/7.15 tff(151,plain,
% 11.15/7.15 (app(app(tptp_fun_W_6(nil, nil), W!49), Y!51) = V!48),
% 11.15/7.15 inference(transitivity,[status(thm)],[150, 35, 34])).
% 11.15/7.15 tff(152,plain,
% 11.15/7.15 (segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49) <=> segmentP(V!48, U!47)),
% 11.15/7.15 inference(monotonicity,[status(thm)],[151, 32])).
% 11.15/7.15 tff(153,plain,
% 11.15/7.15 (segmentP(V!48, U!47) <=> segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49)),
% 11.15/7.15 inference(symmetry,[status(thm)],[152])).
% 11.15/7.15 tff(154,plain,
% 11.15/7.15 ((~segmentP(V!48, U!47)) <=> (~segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49))),
% 11.15/7.15 inference(monotonicity,[status(thm)],[153])).
% 11.15/7.15 tff(155,plain,
% 11.15/7.15 (strictorderedP(U!47) <=> strictorderedP(W!49)),
% 11.15/7.15 inference(monotonicity,[status(thm)],[31])).
% 11.15/7.15 tff(156,plain,
% 11.15/7.15 (strictorderedP(W!49) <=> strictorderedP(U!47)),
% 11.15/7.15 inference(symmetry,[status(thm)],[155])).
% 11.15/7.15 tff(157,plain,
% 11.15/7.15 (strictorderedP(W!49)),
% 11.15/7.15 inference(and_elim,[status(thm)],[30])).
% 11.15/7.15 tff(158,plain,
% 11.15/7.15 (strictorderedP(U!47)),
% 11.15/7.15 inference(modus_ponens,[status(thm)],[157, 156])).
% 11.15/7.15 tff(159,plain,
% 11.15/7.15 ((~(~((~segmentP(V!48, U!47)) | (~strictorderedP(U!47))))) <=> ((~segmentP(V!48, U!47)) | (~strictorderedP(U!47)))),
% 11.15/7.15 inference(rewrite,[status(thm)],[])).
% 11.15/7.15 tff(160,plain,
% 11.15/7.15 ((segmentP(V!48, U!47) & strictorderedP(U!47)) <=> (~((~segmentP(V!48, U!47)) | (~strictorderedP(U!47))))),
% 11.15/7.15 inference(rewrite,[status(thm)],[])).
% 11.15/7.15 tff(161,plain,
% 11.15/7.15 ((~(segmentP(V!48, U!47) & strictorderedP(U!47))) <=> (~(~((~segmentP(V!48, U!47)) | (~strictorderedP(U!47)))))),
% 11.15/7.15 inference(monotonicity,[status(thm)],[160])).
% 11.15/7.15 tff(162,plain,
% 11.15/7.15 ((~(segmentP(V!48, U!47) & strictorderedP(U!47))) <=> ((~segmentP(V!48, U!47)) | (~strictorderedP(U!47)))),
% 11.15/7.15 inference(transitivity,[status(thm)],[161, 159])).
% 11.15/7.15 tff(163,plain,
% 11.15/7.15 (~(segmentP(V!48, U!47) & strictorderedP(U!47))),
% 11.15/7.15 inference(and_elim,[status(thm)],[30])).
% 11.15/7.15 tff(164,plain,
% 11.15/7.15 ((~segmentP(V!48, U!47)) | (~strictorderedP(U!47))),
% 11.15/7.15 inference(modus_ponens,[status(thm)],[163, 162])).
% 11.15/7.15 tff(165,plain,
% 11.15/7.15 (~segmentP(V!48, U!47)),
% 11.15/7.15 inference(unit_resolution,[status(thm)],[164, 158])).
% 11.15/7.15 tff(166,plain,
% 11.15/7.15 (~segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49)),
% 11.15/7.15 inference(modus_ponens,[status(thm)],[165, 154])).
% 11.15/7.15 tff(167,plain,
% 11.15/7.15 (^[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)))))))),
% 11.15/7.15 inference(bind,[status(th)],[])).
% 11.15/7.15 tff(168,plain,
% 11.15/7.15 (![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))))))),
% 11.15/7.15 inference(quant_intro,[status(thm)],[167])).
% 11.15/7.15 tff(169,plain,
% 11.15/7.15 (^[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)))))))),
% 11.15/7.15 inference(bind,[status(th)],[])).
% 11.15/7.15 tff(170,plain,
% 11.15/7.15 (![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))))))),
% 11.15/7.15 inference(quant_intro,[status(thm)],[169])).
% 11.15/7.15 tff(171,plain,
% 11.15/7.15 (![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))))))),
% 11.15/7.15 inference(transitivity,[status(thm)],[170, 168])).
% 11.15/7.16 tff(172,plain,
% 11.15/7.16 (![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))))))),
% 11.15/7.16 inference(rewrite,[status(thm)],[])).
% 11.15/7.16 tff(173,plain,
% 11.15/7.16 (^[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))))))))),
% 11.15/7.16 inference(bind,[status(th)],[])).
% 11.15/7.16 tff(174,plain,
% 11.15/7.16 (![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))))))),
% 11.15/7.16 inference(quant_intro,[status(thm)],[173])).
% 11.15/7.16 tff(175,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')).
% 11.15/7.16 tff(176,plain,
% 11.15/7.16 (![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))))))),
% 11.15/7.16 inference(modus_ponens,[status(thm)],[175, 174])).
% 11.15/7.16 tff(177,plain,
% 11.15/7.16 (![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))))))),
% 11.15/7.16 inference(modus_ponens,[status(thm)],[176, 172])).
% 11.15/7.16 tff(178,plain,(
% 11.15/7.16 ![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))))))),
% 11.15/7.16 inference(skolemize,[status(sab)],[177])).
% 11.15/7.16 tff(179,plain,
% 11.15/7.16 (![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))))))),
% 11.15/7.16 inference(modus_ponens,[status(thm)],[178, 171])).
% 11.15/7.16 tff(180,plain,
% 11.15/7.16 (((~![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))))))),
% 11.15/7.16 inference(rewrite,[status(thm)],[])).
% 11.15/7.16 tff(181,plain,
% 11.15/7.16 (((~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))))))),
% 11.15/7.16 inference(rewrite,[status(thm)],[])).
% 11.15/7.16 tff(182,plain,
% 11.15/7.16 (((~![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)))))))),
% 11.15/7.16 inference(monotonicity,[status(thm)],[181])).
% 11.15/7.16 tff(183,plain,
% 11.15/7.16 (((~![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))))))),
% 11.15/7.16 inference(transitivity,[status(thm)],[182, 180])).
% 11.15/7.16 tff(184,plain,
% 11.15/7.16 ((~![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))))))),
% 11.15/7.16 inference(quant_inst,[status(thm)],[])).
% 11.15/7.16 tff(185,plain,
% 11.15/7.16 ((~![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)))))),
% 11.15/7.16 inference(modus_ponens,[status(thm)],[184, 183])).
% 11.15/7.16 tff(186,plain,
% 11.15/7.16 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 11.15/7.16 inference(unit_resolution,[status(thm)],[185, 179, 36])).
% 11.15/7.16 tff(187,plain,
% 11.15/7.16 (((~![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))))),
% 11.15/7.16 inference(rewrite,[status(thm)],[])).
% 11.15/7.16 tff(188,plain,
% 11.15/7.16 (((~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))))),
% 11.15/7.16 inference(rewrite,[status(thm)],[])).
% 11.15/7.16 tff(189,plain,
% 11.15/7.16 (((~![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)))))),
% 11.15/7.16 inference(monotonicity,[status(thm)],[188])).
% 11.15/7.16 tff(190,plain,
% 11.15/7.16 (((~![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))))),
% 11.15/7.16 inference(transitivity,[status(thm)],[189, 187])).
% 11.15/7.16 tff(191,plain,
% 11.15/7.16 ((~![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)))))),
% 11.15/7.16 inference(quant_inst,[status(thm)],[])).
% 11.15/7.16 tff(192,plain,
% 11.15/7.16 ((~![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)))),
% 11.15/7.17 inference(modus_ponens,[status(thm)],[191, 190])).
% 11.15/7.17 tff(193,plain,
% 11.15/7.17 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 11.15/7.17 inference(unit_resolution,[status(thm)],[192, 36, 186])).
% 11.15/7.17 tff(194,plain,
% 11.15/7.17 (((~![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(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49)))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(tptp_fun_W_6(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49)))),
% 11.15/7.17 inference(rewrite,[status(thm)],[])).
% 11.15/7.17 tff(195,plain,
% 11.15/7.17 ((~![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(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49)))),
% 11.15/7.17 inference(quant_inst,[status(thm)],[])).
% 11.15/7.17 tff(196,plain,
% 11.15/7.17 ((~![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(nil, nil))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49))),
% 11.15/7.17 inference(modus_ponens,[status(thm)],[195, 194])).
% 11.15/7.17 tff(197,plain,
% 11.15/7.17 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49))),
% 11.15/7.17 inference(unit_resolution,[status(thm)],[196, 193, 119])).
% 11.15/7.17 tff(198,plain,
% 11.15/7.17 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 11.15/7.17 inference(bind,[status(th)],[])).
% 11.15/7.17 tff(199,plain,
% 11.15/7.17 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(quant_intro,[status(thm)],[198])).
% 11.15/7.17 tff(200,plain,
% 11.15/7.17 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(rewrite,[status(thm)],[])).
% 11.15/7.17 tff(201,plain,
% 11.15/7.17 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 11.15/7.17 inference(bind,[status(th)],[])).
% 11.15/7.17 tff(202,plain,
% 11.15/7.17 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(quant_intro,[status(thm)],[201])).
% 11.15/7.17 tff(203,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax55')).
% 11.15/7.17 tff(204,plain,
% 11.15/7.17 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(modus_ponens,[status(thm)],[203, 202])).
% 11.15/7.17 tff(205,plain,
% 11.15/7.17 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(modus_ponens,[status(thm)],[204, 200])).
% 11.15/7.17 tff(206,plain,(
% 11.15/7.17 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(skolemize,[status(sab)],[205])).
% 11.15/7.17 tff(207,plain,
% 11.15/7.17 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 11.15/7.17 inference(modus_ponens,[status(thm)],[206, 199])).
% 11.15/7.17 tff(208,plain,
% 11.15/7.17 (((~![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))),
% 11.15/7.17 inference(rewrite,[status(thm)],[])).
% 11.15/7.17 tff(209,plain,
% 11.15/7.17 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 11.15/7.17 inference(quant_inst,[status(thm)],[])).
% 11.15/7.17 tff(210,plain,
% 11.15/7.17 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 11.15/7.17 inference(modus_ponens,[status(thm)],[209, 208])).
% 11.15/7.17 tff(211,plain,
% 11.15/7.17 (segmentP(W!49, W!49)),
% 11.15/7.17 inference(unit_resolution,[status(thm)],[210, 207, 36])).
% 11.15/7.17 tff(212,plain,
% 11.15/7.17 (ssList(Y!51)),
% 11.15/7.17 inference(and_elim,[status(thm)],[30])).
% 11.15/7.17 tff(213,plain,
% 11.15/7.17 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49))) | ((~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49))) | (~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49))),
% 11.20/7.21 inference(rewrite,[status(thm)],[])).
% 11.20/7.21 tff(214,plain,
% 11.20/7.21 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49))) | ((~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49))),
% 11.20/7.21 inference(quant_inst,[status(thm)],[])).
% 11.20/7.21 tff(215,plain,
% 11.20/7.21 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), X), W!49))) | (~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49)),
% 11.20/7.21 inference(modus_ponens,[status(thm)],[214, 213])).
% 11.20/7.21 tff(216,plain,
% 11.20/7.21 (segmentP(app(app(tptp_fun_W_6(nil, nil), W!49), Y!51), W!49)),
% 11.20/7.21 inference(unit_resolution,[status(thm)],[215, 212, 211, 197])).
% 11.20/7.21 tff(217,plain,
% 11.20/7.21 ($false),
% 11.20/7.21 inference(unit_resolution,[status(thm)],[216, 166])).
% 11.20/7.21 % SZS output end Proof
%------------------------------------------------------------------------------