TSTP Solution File: SWC351+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC351+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 11:57:18 EDT 2022
% Result : Theorem 1.66s 1.32s
% Output : Proof 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWC351+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n002.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 00:31:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.66/1.32 % SZS status Theorem
% 1.66/1.32 % SZS output start Proof
% 1.66/1.32 tff(frontsegP_type, type, (
% 1.66/1.32 frontsegP: ( $i * $i ) > $o)).
% 1.66/1.32 tff(tptp_fun_W_49_type, type, (
% 1.66/1.32 tptp_fun_W_49: $i)).
% 1.66/1.32 tff(app_type, type, (
% 1.66/1.32 app: ( $i * $i ) > $i)).
% 1.66/1.32 tff(tptp_fun_Y_51_type, type, (
% 1.66/1.32 tptp_fun_Y_51: $i)).
% 1.66/1.32 tff(tptp_fun_U_47_type, type, (
% 1.66/1.32 tptp_fun_U_47: $i)).
% 1.66/1.32 tff(tptp_fun_V_48_type, type, (
% 1.66/1.32 tptp_fun_V_48: $i)).
% 1.66/1.32 tff(lt_type, type, (
% 1.66/1.32 lt: ( $i * $i ) > $o)).
% 1.66/1.32 tff(cons_type, type, (
% 1.66/1.32 cons: ( $i * $i ) > $i)).
% 1.66/1.32 tff(nil_type, type, (
% 1.66/1.32 nil: $i)).
% 1.66/1.32 tff(ssList_type, type, (
% 1.66/1.32 ssList: $i > $o)).
% 1.66/1.32 tff(ssItem_type, type, (
% 1.66/1.32 ssItem: $i > $o)).
% 1.66/1.32 tff(tptp_fun_X_50_type, type, (
% 1.66/1.32 tptp_fun_X_50: $i)).
% 1.66/1.32 tff(strictorderedP_type, type, (
% 1.66/1.32 strictorderedP: $i > $o)).
% 1.66/1.32 tff(neq_type, type, (
% 1.66/1.32 neq: ( $i * $i ) > $o)).
% 1.66/1.32 tff(1,plain,
% 1.66/1.32 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(2,plain,
% 1.66/1.32 ((ssList(V!48) & (ssList(W!49) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(3,plain,
% 1.66/1.32 ((ssList(W!49) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(4,plain,
% 1.66/1.32 (((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))) <=> ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(5,plain,
% 1.66/1.32 (((~(~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)))))))),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(6,plain,
% 1.66/1.32 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(7,plain,
% 1.66/1.32 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(8,plain,
% 1.66/1.32 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(9,plain,
% 1.66/1.32 ((~(~neq(V!48, nil))) <=> neq(V!48, nil)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(10,plain,
% 1.66/1.32 (((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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)))))))) <=> ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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))))))))),
% 1.66/1.32 inference(monotonicity,[status(thm)],[9, 8, 7, 6, 5])).
% 1.66/1.32 tff(11,plain,
% 1.66/1.32 (((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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)))))))) <=> ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(transitivity,[status(thm)],[10, 4])).
% 1.66/1.32 tff(12,plain,
% 1.66/1.32 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(13,plain,
% 1.66/1.32 (((~(~ssList(W!49))) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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))))))))),
% 1.66/1.32 inference(monotonicity,[status(thm)],[12, 11])).
% 1.66/1.32 tff(14,plain,
% 1.66/1.32 (((~(~ssList(W!49))) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(transitivity,[status(thm)],[13, 3])).
% 1.66/1.32 tff(15,plain,
% 1.66/1.32 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(16,plain,
% 1.66/1.32 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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))))))))),
% 1.66/1.32 inference(monotonicity,[status(thm)],[15, 14])).
% 1.66/1.32 tff(17,plain,
% 1.66/1.32 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.32 inference(transitivity,[status(thm)],[16, 2])).
% 1.66/1.32 tff(18,plain,
% 1.66/1.32 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.66/1.32 inference(rewrite,[status(thm)],[])).
% 1.66/1.32 tff(19,plain,
% 1.66/1.32 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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))))))))),
% 1.66/1.33 inference(monotonicity,[status(thm)],[18, 17])).
% 1.66/1.33 tff(20,plain,
% 1.66/1.33 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~neq(V!48, nil))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~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) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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)))))))),
% 1.66/1.33 inference(transitivity,[status(thm)],[19, 1])).
% 1.66/1.33 tff(21,plain,
% 1.66/1.33 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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)))))))))))),
% 1.66/1.33 inference(rewrite,[status(thm)],[])).
% 1.66/1.33 tff(22,plain,
% 1.66/1.33 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~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)))))))) | frontsegP(V, U)) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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)))))))))))),
% 1.66/1.33 inference(rewrite,[status(thm)],[])).
% 1.66/1.33 tff(23,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~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)))))))) | frontsegP(V, U)) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 1.66/1.33 tff(24,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.66/1.33 tff(25,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[24, 21])).
% 1.66/1.33 tff(26,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.66/1.33 tff(27,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[26, 21])).
% 1.66/1.33 tff(28,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[27, 21])).
% 1.66/1.33 tff(29,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[28, 21])).
% 1.66/1.33 tff(30,plain,
% 1.66/1.33 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (frontsegP(V, U) | ((~(nil = X)) & (nil = W)) | (~neq(V, nil)) | (~(U = W)) | (~(V = X)) | (~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))))))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[29, 21])).
% 1.66/1.33 tff(31,plain,
% 1.66/1.33 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~frontsegP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & neq(V!48, nil) & (U!47 = W!49) & (V!48 = X!50) & 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))))))),
% 1.66/1.33 inference(modus_ponens,[status(thm)],[30, 20])).
% 1.66/1.33 tff(32,plain,
% 1.66/1.33 (U!47 = W!49),
% 1.66/1.33 inference(and_elim,[status(thm)],[31])).
% 1.66/1.33 tff(33,plain,
% 1.66/1.33 (W!49 = U!47),
% 1.66/1.33 inference(symmetry,[status(thm)],[32])).
% 1.66/1.33 tff(34,plain,
% 1.66/1.33 (V!48 = X!50),
% 1.66/1.33 inference(and_elim,[status(thm)],[31])).
% 1.66/1.33 tff(35,plain,
% 1.66/1.33 (X!50 = V!48),
% 1.66/1.33 inference(symmetry,[status(thm)],[34])).
% 1.66/1.33 tff(36,plain,
% 1.66/1.33 (app(W!49, Y!51) = X!50),
% 1.74/1.33 inference(and_elim,[status(thm)],[31])).
% 1.74/1.33 tff(37,plain,
% 1.74/1.33 (app(W!49, Y!51) = V!48),
% 1.74/1.33 inference(transitivity,[status(thm)],[36, 35])).
% 1.74/1.33 tff(38,plain,
% 1.74/1.33 (frontsegP(app(W!49, Y!51), W!49) <=> frontsegP(V!48, U!47)),
% 1.74/1.33 inference(monotonicity,[status(thm)],[37, 33])).
% 1.74/1.33 tff(39,plain,
% 1.74/1.33 (frontsegP(V!48, U!47) <=> frontsegP(app(W!49, Y!51), W!49)),
% 1.74/1.33 inference(symmetry,[status(thm)],[38])).
% 1.74/1.33 tff(40,plain,
% 1.74/1.33 ((~frontsegP(V!48, U!47)) <=> (~frontsegP(app(W!49, Y!51), W!49))),
% 1.74/1.33 inference(monotonicity,[status(thm)],[39])).
% 1.74/1.33 tff(41,plain,
% 1.74/1.33 (~frontsegP(V!48, U!47)),
% 1.74/1.33 inference(and_elim,[status(thm)],[31])).
% 1.74/1.33 tff(42,plain,
% 1.74/1.33 (~frontsegP(app(W!49, Y!51), W!49)),
% 1.74/1.33 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.74/1.33 tff(43,plain,
% 1.74/1.33 (ssList(W!49)),
% 1.74/1.33 inference(and_elim,[status(thm)],[31])).
% 1.74/1.33 tff(44,plain,
% 1.74/1.33 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 1.74/1.33 inference(bind,[status(th)],[])).
% 1.74/1.33 tff(45,plain,
% 1.74/1.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.33 inference(quant_intro,[status(thm)],[44])).
% 1.74/1.33 tff(46,plain,
% 1.74/1.33 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 1.74/1.33 inference(bind,[status(th)],[])).
% 1.74/1.33 tff(47,plain,
% 1.74/1.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.33 inference(quant_intro,[status(thm)],[46])).
% 1.74/1.33 tff(48,plain,
% 1.74/1.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.33 inference(transitivity,[status(thm)],[47, 45])).
% 1.74/1.33 tff(49,plain,
% 1.74/1.33 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.33 inference(rewrite,[status(thm)],[])).
% 1.74/1.33 tff(50,plain,
% 1.74/1.33 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((frontsegP(U, V) => frontsegP(app(U, W), V)) <=> ((~frontsegP(U, V)) | frontsegP(app(U, W), V))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))))), rewrite((ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), (![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> (ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), rewrite((ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))))),
% 1.74/1.34 inference(bind,[status(th)],[])).
% 1.74/1.34 tff(51,plain,
% 1.74/1.34 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.34 inference(quant_intro,[status(thm)],[50])).
% 1.74/1.34 tff(52,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax43')).
% 1.74/1.34 tff(53,plain,
% 1.74/1.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.34 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.74/1.34 tff(54,plain,
% 1.74/1.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.34 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.74/1.34 tff(55,plain,(
% 1.74/1.34 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.34 inference(skolemize,[status(sab)],[54])).
% 1.74/1.34 tff(56,plain,
% 1.74/1.34 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 1.74/1.34 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.74/1.34 tff(57,plain,
% 1.74/1.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))),
% 1.74/1.34 inference(rewrite,[status(thm)],[])).
% 1.74/1.34 tff(58,plain,
% 1.74/1.34 (((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V))))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))),
% 1.74/1.34 inference(rewrite,[status(thm)],[])).
% 1.74/1.34 tff(59,plain,
% 1.74/1.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))))),
% 1.74/1.34 inference(monotonicity,[status(thm)],[58])).
% 1.74/1.34 tff(60,plain,
% 1.74/1.34 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V)))))),
% 1.74/1.34 inference(transitivity,[status(thm)],[59, 57])).
% 1.74/1.34 tff(61,plain,
% 1.74/1.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(W!49, W), V) | (~ssList(W)) | (~frontsegP(W!49, V)))))),
% 1.74/1.34 inference(quant_inst,[status(thm)],[])).
% 1.74/1.34 tff(62,plain,
% 1.74/1.34 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))),
% 1.74/1.34 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.74/1.34 tff(63,plain,
% 1.74/1.34 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))),
% 1.74/1.34 inference(unit_resolution,[status(thm)],[62, 56, 43])).
% 1.74/1.34 tff(64,plain,
% 1.74/1.34 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))),
% 1.74/1.34 inference(rewrite,[status(thm)],[])).
% 1.74/1.34 tff(65,plain,
% 1.74/1.34 (((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49)))) <=> ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))),
% 1.74/1.34 inference(rewrite,[status(thm)],[])).
% 1.74/1.34 tff(66,plain,
% 1.74/1.34 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))))),
% 1.74/1.34 inference(monotonicity,[status(thm)],[65])).
% 1.74/1.34 tff(67,plain,
% 1.74/1.34 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49)))),
% 1.74/1.34 inference(transitivity,[status(thm)],[66, 64])).
% 1.74/1.34 tff(68,plain,
% 1.74/1.34 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), W!49) | (~frontsegP(W!49, W!49))))),
% 1.74/1.34 inference(quant_inst,[status(thm)],[])).
% 1.74/1.34 tff(69,plain,
% 1.74/1.34 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(W!49, W), V) | (~frontsegP(W!49, V))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))),
% 1.74/1.34 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.74/1.34 tff(70,plain,
% 1.74/1.34 (![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))),
% 1.74/1.34 inference(unit_resolution,[status(thm)],[69, 43, 63])).
% 1.74/1.34 tff(71,plain,
% 1.74/1.34 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 1.74/1.34 inference(bind,[status(th)],[])).
% 1.74/1.34 tff(72,plain,
% 1.74/1.34 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.34 inference(quant_intro,[status(thm)],[71])).
% 1.74/1.34 tff(73,plain,
% 1.74/1.34 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.35 inference(rewrite,[status(thm)],[])).
% 1.74/1.35 tff(74,plain,
% 1.74/1.35 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 1.74/1.35 inference(bind,[status(th)],[])).
% 1.74/1.35 tff(75,plain,
% 1.74/1.35 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.35 inference(quant_intro,[status(thm)],[74])).
% 1.74/1.35 tff(76,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax42')).
% 1.74/1.35 tff(77,plain,
% 1.74/1.35 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.35 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.74/1.35 tff(78,plain,
% 1.74/1.35 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.35 inference(modus_ponens,[status(thm)],[77, 73])).
% 1.74/1.35 tff(79,plain,(
% 1.74/1.35 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.35 inference(skolemize,[status(sab)],[78])).
% 1.74/1.35 tff(80,plain,
% 1.74/1.35 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 1.74/1.35 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.74/1.35 tff(81,plain,
% 1.74/1.35 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49))),
% 1.74/1.35 inference(rewrite,[status(thm)],[])).
% 1.74/1.35 tff(82,plain,
% 1.74/1.35 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))),
% 1.74/1.35 inference(quant_inst,[status(thm)],[])).
% 1.74/1.35 tff(83,plain,
% 1.74/1.35 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49)),
% 1.74/1.35 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.74/1.35 tff(84,plain,
% 1.74/1.35 (frontsegP(W!49, W!49)),
% 1.74/1.35 inference(unit_resolution,[status(thm)],[83, 80, 43])).
% 1.74/1.35 tff(85,plain,
% 1.74/1.35 (ssList(Y!51)),
% 1.74/1.35 inference(and_elim,[status(thm)],[31])).
% 1.74/1.35 tff(86,plain,
% 1.74/1.35 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | ((~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | (~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49))),
% 1.74/1.35 inference(rewrite,[status(thm)],[])).
% 1.74/1.35 tff(87,plain,
% 1.74/1.35 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | ((~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49))),
% 1.74/1.35 inference(quant_inst,[status(thm)],[])).
% 1.74/1.35 tff(88,plain,
% 1.74/1.35 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, W), W!49))) | (~ssList(Y!51)) | (~frontsegP(W!49, W!49)) | frontsegP(app(W!49, Y!51), W!49)),
% 1.74/1.35 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.74/1.35 tff(89,plain,
% 1.74/1.35 (frontsegP(app(W!49, Y!51), W!49)),
% 1.74/1.35 inference(unit_resolution,[status(thm)],[88, 85, 84, 70])).
% 1.74/1.35 tff(90,plain,
% 1.74/1.35 ($false),
% 1.74/1.35 inference(unit_resolution,[status(thm)],[89, 42])).
% 1.74/1.35 % SZS output end Proof
%------------------------------------------------------------------------------