TSTP Solution File: SWC009+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC009+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 11:54:37 EDT 2022
% Result : Theorem 1.11s 0.95s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC009+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 20:35:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.11/0.95 % SZS status Theorem
% 1.11/0.95 % SZS output start Proof
% 1.11/0.95 tff(tptp_fun_V_48_type, type, (
% 1.11/0.95 tptp_fun_V_48: $i)).
% 1.11/0.95 tff(app_type, type, (
% 1.11/0.95 app: ( $i * $i ) > $i)).
% 1.11/0.95 tff(nil_type, type, (
% 1.11/0.95 nil: $i)).
% 1.11/0.95 tff(tptp_fun_X2_51_type, type, (
% 1.11/0.95 tptp_fun_X2_51: $i)).
% 1.11/0.95 tff(tptp_fun_W_49_type, type, (
% 1.11/0.95 tptp_fun_W_49: $i)).
% 1.11/0.95 tff(tptp_fun_X_50_type, type, (
% 1.11/0.95 tptp_fun_X_50: $i)).
% 1.11/0.95 tff(lt_type, type, (
% 1.11/0.95 lt: ( $i * $i ) > $o)).
% 1.11/0.95 tff(cons_type, type, (
% 1.11/0.95 cons: ( $i * $i ) > $i)).
% 1.11/0.95 tff(ssList_type, type, (
% 1.11/0.95 ssList: $i > $o)).
% 1.11/0.95 tff(ssItem_type, type, (
% 1.11/0.95 ssItem: $i > $o)).
% 1.11/0.95 tff(strictorderedP_type, type, (
% 1.11/0.95 strictorderedP: $i > $o)).
% 1.11/0.95 tff(tptp_fun_U_47_type, type, (
% 1.11/0.95 tptp_fun_U_47: $i)).
% 1.11/0.95 tff(1,plain,
% 1.11/0.95 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(2,plain,
% 1.11/0.95 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(3,plain,
% 1.11/0.95 ((ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(4,plain,
% 1.11/0.95 (((~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & (strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(5,plain,
% 1.11/0.95 (((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))) <=> (strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(6,plain,
% 1.11/0.95 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(7,plain,
% 1.11/0.95 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(8,plain,
% 1.11/0.95 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(9,plain,
% 1.11/0.95 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & (strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[8, 7, 6, 5])).
% 1.11/0.95 tff(10,plain,
% 1.11/0.95 (((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))) <=> ((~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(transitivity,[status(thm)],[9, 4])).
% 1.11/0.95 tff(11,plain,
% 1.11/0.95 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(12,plain,
% 1.11/0.95 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))) <=> (ssList(W!49) & ((~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[11, 10])).
% 1.11/0.95 tff(13,plain,
% 1.11/0.95 (((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))) <=> (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.95 inference(transitivity,[status(thm)],[12, 3])).
% 1.11/0.95 tff(14,plain,
% 1.11/0.95 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(15,plain,
% 1.11/0.95 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[14, 13])).
% 1.11/0.95 tff(16,plain,
% 1.11/0.95 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.96 inference(transitivity,[status(thm)],[15, 2])).
% 1.11/0.96 tff(17,plain,
% 1.11/0.96 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(18,plain,
% 1.11/0.96 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[17, 16])).
% 1.11/0.96 tff(19,plain,
% 1.11/0.96 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, X2!51) = X!50))) & (~(~ssList(X2!51))) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3)))))))),
% 1.11/0.96 inference(transitivity,[status(thm)],[18, 1])).
% 1.11/0.96 tff(20,plain,
% 1.11/0.96 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3)))))))))))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(21,plain,
% 1.11/0.96 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ![X2: $i] : (ssList(X2) => (((~(app(W, X2) = X)) | (~strictorderedP(W))) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = X2)) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(X6, cons(X5, nil)) = W)) & lt(X5, X3)))))))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3)))))))))))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 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) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ![X2: $i] : (ssList(X2) => (((~(app(W, X2) = X)) | (~strictorderedP(W))) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = X2)) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(X6, cons(X5, nil)) = W)) & lt(X5, X3)))))))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 1.11/0.96 tff(23,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.11/0.96 tff(24,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[23, 20])).
% 1.11/0.96 tff(25,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.11/0.96 tff(26,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[25, 20])).
% 1.11/0.96 tff(27,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[26, 20])).
% 1.11/0.96 tff(28,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.11/0.96 tff(29,plain,
% 1.11/0.96 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ![X2: $i] : ((~strictorderedP(W)) | (~(app(W, X2) = X)) | (~ssList(X2)) | ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = X2) & ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X5, nil)) = W) & lt(X5, X3))))))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[28, 20])).
% 1.11/0.96 tff(30,plain,
% 1.11/0.96 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & strictorderedP(W!49) & (app(W!49, X2!51) = X!50) & ssList(X2!51) & ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssList(X4)) | (~(app(cons(X3, nil), X4) = X2!51)) | ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X5, nil)) = W!49) & lt(X5, X3))))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[29, 19])).
% 1.11/0.96 tff(31,plain,
% 1.11/0.96 (V!48 = X!50),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(32,plain,
% 1.11/0.96 (X!50 = V!48),
% 1.11/0.96 inference(symmetry,[status(thm)],[31])).
% 1.11/0.96 tff(33,plain,
% 1.11/0.96 (ssList(X!50)),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(34,plain,
% 1.11/0.96 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(35,plain,
% 1.11/0.96 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[34])).
% 1.11/0.96 tff(36,plain,
% 1.11/0.96 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(37,plain,
% 1.11/0.96 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(38,plain,
% 1.11/0.96 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[37])).
% 1.11/0.96 tff(39,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 1.11/0.96 tff(40,plain,
% 1.11/0.96 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.11/0.96 tff(41,plain,
% 1.11/0.96 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.11/0.96 tff(42,plain,(
% 1.11/0.96 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(skolemize,[status(sab)],[41])).
% 1.11/0.96 tff(43,plain,
% 1.11/0.96 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.11/0.96 tff(44,plain,
% 1.11/0.96 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(45,plain,
% 1.11/0.96 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(46,plain,
% 1.11/0.96 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.11/0.96 tff(47,plain,
% 1.11/0.96 (app(X!50, nil) = X!50),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 1.11/0.96 tff(48,plain,
% 1.11/0.96 (app(W!49, X2!51) = X!50),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(49,plain,
% 1.11/0.96 (app(app(W!49, X2!51), nil) = app(X!50, nil)),
% 1.11/0.96 inference(monotonicity,[status(thm)],[48])).
% 1.11/0.96 tff(50,plain,
% 1.11/0.96 (app(app(W!49, X2!51), nil) = V!48),
% 1.11/0.96 inference(transitivity,[status(thm)],[49, 47, 32])).
% 1.11/0.96 tff(51,plain,
% 1.11/0.96 (U!47 = W!49),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(52,plain,
% 1.11/0.96 (W!49 = U!47),
% 1.11/0.96 inference(symmetry,[status(thm)],[51])).
% 1.11/0.96 tff(53,plain,
% 1.11/0.96 (ssList(W!49)),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(54,plain,
% 1.11/0.96 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(W!49)) | (app(W!49, nil) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(W!49)) | (app(W!49, nil) = W!49))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(55,plain,
% 1.11/0.96 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(W!49)) | (app(W!49, nil) = W!49))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(56,plain,
% 1.11/0.96 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(W!49)) | (app(W!49, nil) = W!49)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.11/0.96 tff(57,plain,
% 1.11/0.96 (app(W!49, nil) = W!49),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[56, 43, 53])).
% 1.11/0.96 tff(58,plain,
% 1.11/0.96 (app(W!49, nil) = U!47),
% 1.11/0.96 inference(transitivity,[status(thm)],[57, 52])).
% 1.11/0.96 tff(59,plain,
% 1.11/0.96 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(60,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[59])).
% 1.11/0.96 tff(61,plain,
% 1.11/0.96 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(62,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[61])).
% 1.11/0.96 tff(63,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(transitivity,[status(thm)],[62, 60])).
% 1.11/0.96 tff(64,plain,
% 1.11/0.96 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(65,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[64])).
% 1.11/0.96 tff(66,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(67,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.11/0.96 tff(68,plain,
% 1.11/0.96 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[67, 63])).
% 1.11/0.96 tff(69,plain,
% 1.11/0.96 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47)))))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(70,plain,
% 1.11/0.96 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47)))))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(71,plain,
% 1.11/0.96 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.11/0.96 tff(72,plain,
% 1.11/0.96 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[71, 53, 68])).
% 1.11/0.96 tff(73,plain,
% 1.11/0.96 (ssList(X2!51)),
% 1.11/0.96 inference(and_elim,[status(thm)],[30])).
% 1.11/0.96 tff(74,plain,
% 1.11/0.96 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48))))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(75,plain,
% 1.11/0.96 (((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, X2!51), X1) = V!48)) | (~(app(W!49, X1) = U!47)))) <=> ((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48))))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(76,plain,
% 1.11/0.97 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, X2!51), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[75])).
% 1.11/0.97 tff(77,plain,
% 1.11/0.97 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, X2!51), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48))))),
% 1.11/0.97 inference(transitivity,[status(thm)],[76, 74])).
% 1.11/0.97 tff(78,plain,
% 1.11/0.97 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, X2!51), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(79,plain,
% 1.11/0.97 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(X2!51)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.11/0.97 tff(80,plain,
% 1.11/0.97 (![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[79, 73, 72])).
% 1.11/0.97 tff(81,plain,
% 1.11/0.97 (ssList(nil) <=> ssList(nil)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(82,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 1.11/0.97 tff(83,plain,
% 1.11/0.97 (ssList(nil)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.11/0.97 tff(84,plain,
% 1.11/0.97 (((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))) | ((~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, X2!51), nil) = V!48)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))) | (~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, X2!51), nil) = V!48)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(85,plain,
% 1.11/0.97 ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))) | ((~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, X2!51), nil) = V!48)))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(86,plain,
% 1.11/0.97 ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X2!51), X1) = V!48)))) | (~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, X2!51), nil) = V!48))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.11/0.97 tff(87,plain,
% 1.11/0.97 (~(app(app(W!49, X2!51), nil) = V!48)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[86, 83, 80, 58])).
% 1.11/0.97 tff(88,plain,
% 1.11/0.97 ($false),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[87, 50])).
% 1.11/0.97 % SZS output end Proof
%------------------------------------------------------------------------------