%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC402+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 05:31:08 AM UTC 2025
% Result : Theorem 19.05s 19.23s
% Output : Proof 19.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWC402+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 09:14:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 19.05/19.23 % SZS status Theorem
% 19.05/19.23 % SZS output start Proof
% 19.05/19.23 tff(memberP_type, type, (
% 19.05/19.23 memberP: ( $i * $i ) > $o)).
% 19.05/19.23 tff(tptp_fun_X9_49_type, type, (
% 19.05/19.23 tptp_fun_X9_49: $i)).
% 19.05/19.23 tff(app_type, type, (
% 19.05/19.23 app: ( $i * $i ) > $i)).
% 19.05/19.23 tff(tptp_fun_Z_48_type, type, (
% 19.05/19.23 tptp_fun_Z_48: $i)).
% 19.05/19.23 tff(tptp_fun_U_45_type, type, (
% 19.05/19.23 tptp_fun_U_45: $i)).
% 19.05/19.23 tff(tptp_fun_Y_47_type, type, (
% 19.05/19.23 tptp_fun_Y_47: $i)).
% 19.05/19.23 tff(tptp_fun_V_46_type, type, (
% 19.05/19.23 tptp_fun_V_46: $i)).
% 19.05/19.23 tff(ssItem_type, type, (
% 19.05/19.23 ssItem: $i > $o)).
% 19.05/19.23 tff(leq_type, type, (
% 19.05/19.23 leq: ( $i * $i ) > $o)).
% 19.05/19.23 tff(cons_type, type, (
% 19.05/19.23 cons: ( $i * $i ) > $i)).
% 19.05/19.23 tff(nil_type, type, (
% 19.05/19.23 nil: $i)).
% 19.05/19.23 tff(ssList_type, type, (
% 19.05/19.23 ssList: $i > $o)).
% 19.05/19.23 tff(totalorderedP_type, type, (
% 19.05/19.23 totalorderedP: $i > $o)).
% 19.05/19.23 tff(1,plain,
% 19.05/19.23 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(2,plain,
% 19.05/19.23 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5))))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(3,plain,
% 19.05/19.23 ((~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))) <=> (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(4,plain,
% 19.05/19.23 ((ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) <=> (ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(5,plain,
% 19.05/19.23 ((ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5))))))) <=> (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(6,plain,
% 19.05/19.23 ((ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) <=> (ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5))))))))),
% 19.05/19.23 inference(monotonicity,[status(thm)],[5])).
% 19.05/19.23 tff(7,plain,
% 19.05/19.23 ((ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) <=> (ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))),
% 19.05/19.23 inference(transitivity,[status(thm)],[6, 4])).
% 19.05/19.23 tff(8,plain,
% 19.05/19.23 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5))))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))),
% 19.05/19.23 inference(monotonicity,[status(thm)],[7, 3])).
% 19.05/19.23 tff(9,plain,
% 19.05/19.23 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49))))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))),
% 19.05/19.23 inference(transitivity,[status(thm)],[8, 2])).
% 19.05/19.23 tff(10,plain,
% 19.05/19.23 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49))))))),
% 19.05/19.23 inference(monotonicity,[status(thm)],[9])).
% 19.05/19.23 tff(11,plain,
% 19.05/19.23 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))))) & ssList(U!45) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))))),
% 19.05/19.23 inference(transitivity,[status(thm)],[10, 1])).
% 19.05/19.23 tff(12,plain,
% 19.05/19.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9))))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(13,plain,
% 19.05/19.23 ((~![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)) | (~(app(app(Y, W), Z) = X))) | (~totalorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = W)) & leq(X1, X3)))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(cons(X5, nil), X6) = Z)) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : ((ssList(X8) & (app(X8, cons(X7, nil)) = W)) & leq(X7, X5)))))))) | ![X9: $i] : (((~ssItem(X9)) | (~memberP(U, X9))) | memberP(V, X9))) | ((~(nil = X)) & (nil = W))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9))))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(14,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)) | (~(app(app(Y, W), Z) = X))) | (~totalorderedP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : ((ssList(X4) & (app(cons(X3, nil), X4) = W)) & leq(X1, X3)))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : ((ssList(X6) & (app(cons(X5, nil), X6) = Z)) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : ((ssList(X8) & (app(X8, cons(X7, nil)) = W)) & leq(X7, X5)))))))) | ![X9: $i] : (((~ssItem(X9)) | (~memberP(U, X9))) | memberP(V, X9))) | ((~(nil = X)) & (nil = W))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 19.05/19.23 tff(15,plain,
% 19.05/19.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[14, 13])).
% 19.05/19.23 tff(16,plain,
% 19.05/19.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[15, 12])).
% 19.05/19.23 tff(17,plain,
% 19.05/19.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[16, 12])).
% 19.05/19.23 tff(18,plain,
% 19.05/19.23 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | (~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssItem(X3) & ?[X4: $i] : (ssList(X4) & (app(cons(X3, nil), X4) = U) & leq(X1, X3))))) | ?[X5: $i] : (ssItem(X5) & ?[X6: $i] : (ssList(X6) & (app(cons(X5, nil), X6) = Z) & ?[X7: $i] : (ssItem(X7) & ?[X8: $i] : (ssList(X8) & (app(X8, cons(X7, nil)) = U) & leq(X7, X5))))))) | (~ssList(U)) | ![X9: $i] : (memberP(V, X9) | (~ssItem(X9)) | (~memberP(U, X9)))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[17, 12])).
% 19.05/19.23 tff(19,plain,
% 19.05/19.23 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & ssList(Z!48) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : (~(ssList(X4) & (app(cons(X3, nil), X4) = U!45) & leq(X1, X3)))))) & ![X5: $i] : ((~ssItem(X5)) | ![X6: $i] : ((~ssList(X6)) | (~(app(cons(X5, nil), X6) = Z!48)) | ![X7: $i] : ((~ssItem(X7)) | ![X8: $i] : (~(ssList(X8) & (app(X8, cons(X7, nil)) = U!45) & leq(X7, X5)))))) & (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[18, 11])).
% 19.05/19.23 tff(20,plain,
% 19.05/19.23 (app(app(Y!47, U!45), Z!48) = V!46),
% 19.05/19.23 inference(and_elim,[status(thm)],[19])).
% 19.05/19.23 tff(21,plain,
% 19.05/19.23 (memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> memberP(V!46, X9!49)),
% 19.05/19.23 inference(monotonicity,[status(thm)],[20])).
% 19.05/19.23 tff(22,plain,
% 19.05/19.23 (memberP(V!46, X9!49) <=> memberP(app(app(Y!47, U!45), Z!48), X9!49)),
% 19.05/19.23 inference(symmetry,[status(thm)],[21])).
% 19.05/19.23 tff(23,plain,
% 19.05/19.23 ((~memberP(V!46, X9!49)) <=> (~memberP(app(app(Y!47, U!45), Z!48), X9!49))),
% 19.05/19.23 inference(monotonicity,[status(thm)],[22])).
% 19.05/19.23 tff(24,plain,
% 19.05/19.23 (~(memberP(V!46, X9!49) | (~ssItem(X9!49)) | (~memberP(U!45, X9!49)))),
% 19.05/19.23 inference(and_elim,[status(thm)],[19])).
% 19.05/19.23 tff(25,plain,
% 19.05/19.23 (~memberP(V!46, X9!49)),
% 19.05/19.23 inference(or_elim,[status(thm)],[24])).
% 19.05/19.23 tff(26,plain,
% 19.05/19.23 (~memberP(app(app(Y!47, U!45), Z!48), X9!49)),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[25, 23])).
% 19.05/19.23 tff(27,plain,
% 19.05/19.23 (ssList(Y!47)),
% 19.05/19.23 inference(and_elim,[status(thm)],[19])).
% 19.05/19.23 tff(28,plain,
% 19.05/19.23 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 19.05/19.23 inference(bind,[status(th)],[])).
% 19.05/19.23 tff(29,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(quant_intro,[status(thm)],[28])).
% 19.05/19.23 tff(30,plain,
% 19.05/19.23 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 19.05/19.23 inference(bind,[status(th)],[])).
% 19.05/19.23 tff(31,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(quant_intro,[status(thm)],[30])).
% 19.05/19.23 tff(32,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(transitivity,[status(thm)],[31, 29])).
% 19.05/19.23 tff(33,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(34,plain,
% 19.05/19.23 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ssList(app(U, V))) <=> ((~ssList(V)) | ssList(app(U, V))))), (![V: $i] : (ssList(V) => ssList(app(U, V))) <=> ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))))),
% 19.05/19.23 inference(bind,[status(th)],[])).
% 19.05/19.23 tff(35,plain,
% 19.05/19.23 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(quant_intro,[status(thm)],[34])).
% 19.05/19.23 tff(36,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax26')).
% 19.05/19.23 tff(37,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[36, 35])).
% 19.05/19.23 tff(38,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[37, 33])).
% 19.05/19.23 tff(39,plain,(
% 19.05/19.23 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(skolemize,[status(sab)],[38])).
% 19.05/19.23 tff(40,plain,
% 19.05/19.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[39, 32])).
% 19.05/19.23 tff(41,plain,
% 19.05/19.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(42,plain,
% 19.05/19.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V))))),
% 19.05/19.23 inference(quant_inst,[status(thm)],[])).
% 19.05/19.23 tff(43,plain,
% 19.05/19.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[42, 41])).
% 19.05/19.23 tff(44,plain,
% 19.05/19.23 (![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))),
% 19.05/19.23 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 19.05/19.23 tff(45,plain,
% 19.05/19.23 (ssList(U!45)),
% 19.05/19.23 inference(and_elim,[status(thm)],[19])).
% 19.05/19.23 tff(46,plain,
% 19.05/19.23 (((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | ((~ssList(U!45)) | ssList(app(Y!47, U!45)))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | (~ssList(U!45)) | ssList(app(Y!47, U!45)))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(47,plain,
% 19.05/19.23 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | ((~ssList(U!45)) | ssList(app(Y!47, U!45)))),
% 19.05/19.23 inference(quant_inst,[status(thm)],[])).
% 19.05/19.23 tff(48,plain,
% 19.05/19.23 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | (~ssList(U!45)) | ssList(app(Y!47, U!45))),
% 19.05/19.23 inference(modus_ponens,[status(thm)],[47, 46])).
% 19.05/19.23 tff(49,plain,
% 19.05/19.23 (ssList(app(Y!47, U!45))),
% 19.05/19.23 inference(unit_resolution,[status(thm)],[48, 45, 44])).
% 19.05/19.23 tff(50,plain,
% 19.05/19.23 (ssItem(X9!49)),
% 19.05/19.23 inference(or_elim,[status(thm)],[24])).
% 19.05/19.23 tff(51,plain,
% 19.05/19.23 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 19.05/19.23 inference(bind,[status(th)],[])).
% 19.05/19.23 tff(52,plain,
% 19.05/19.23 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.23 inference(quant_intro,[status(thm)],[51])).
% 19.05/19.23 tff(53,plain,
% 19.05/19.23 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))),
% 19.05/19.23 inference(bind,[status(th)],[])).
% 19.05/19.23 tff(54,plain,
% 19.05/19.23 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.23 inference(quant_intro,[status(thm)],[53])).
% 19.05/19.23 tff(55,plain,
% 19.05/19.23 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.23 inference(transitivity,[status(thm)],[54, 52])).
% 19.05/19.23 tff(56,plain,
% 19.05/19.23 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.23 inference(rewrite,[status(thm)],[])).
% 19.05/19.23 tff(57,plain,
% 19.05/19.23 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))) <=> (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> (ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), rewrite((ssList(W) => (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))), ((ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), (![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))), ((ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))))),
% 19.05/19.24 inference(bind,[status(th)],[])).
% 19.05/19.24 tff(58,plain,
% 19.05/19.24 (![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.24 inference(quant_intro,[status(thm)],[57])).
% 19.05/19.24 tff(59,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (memberP(app(V, W), U) <=> (memberP(V, U) | memberP(W, U))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax36')).
% 19.05/19.24 tff(60,plain,
% 19.05/19.24 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[59, 58])).
% 19.05/19.24 tff(61,plain,
% 19.05/19.24 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[60, 56])).
% 19.05/19.24 tff(62,plain,(
% 19.05/19.24 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.24 inference(skolemize,[status(sab)],[61])).
% 19.05/19.24 tff(63,plain,
% 19.05/19.24 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[62, 55])).
% 19.05/19.24 tff(64,plain,
% 19.05/19.24 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X9!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X9!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49))))))),
% 19.05/19.24 inference(rewrite,[status(thm)],[])).
% 19.05/19.24 tff(65,plain,
% 19.05/19.24 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | ((~ssItem(X9!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49))))))),
% 19.05/19.24 inference(quant_inst,[status(thm)],[])).
% 19.05/19.24 tff(66,plain,
% 19.05/19.24 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), U) <=> (memberP(W, U) | memberP(V, U))))))) | (~ssItem(X9!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[65, 64])).
% 19.05/19.24 tff(67,plain,
% 19.05/19.24 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[66, 63, 50])).
% 19.05/19.24 tff(68,plain,
% 19.05/19.24 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | ((~ssList(app(Y!47, U!45))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | (~ssList(app(Y!47, U!45))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49)))))),
% 19.05/19.24 inference(rewrite,[status(thm)],[])).
% 19.05/19.24 tff(69,plain,
% 19.05/19.24 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | ((~ssList(app(Y!47, U!45))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49)))))),
% 19.05/19.24 inference(quant_inst,[status(thm)],[])).
% 19.05/19.24 tff(70,plain,
% 19.05/19.24 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | (~ssList(app(Y!47, U!45))) | ![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49))))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[69, 68])).
% 19.05/19.24 tff(71,plain,
% 19.05/19.24 (![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49))))),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[70, 67, 49])).
% 19.05/19.24 tff(72,plain,
% 19.05/19.24 (ssList(Z!48)),
% 19.05/19.24 inference(and_elim,[status(thm)],[19])).
% 19.05/19.24 tff(73,plain,
% 19.05/19.24 (((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49))))) | ((~ssList(Z!48)) | (memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49))))) | (~ssList(Z!48)) | (memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49))))),
% 19.05/19.24 inference(rewrite,[status(thm)],[])).
% 19.05/19.24 tff(74,plain,
% 19.05/19.24 ((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49))))) | ((~ssList(Z!48)) | (memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49))))),
% 19.05/19.24 inference(quant_inst,[status(thm)],[])).
% 19.05/19.24 tff(75,plain,
% 19.05/19.24 ((~![W: $i] : ((~ssList(W)) | (memberP(app(app(Y!47, U!45), W), X9!49) <=> (memberP(W, X9!49) | memberP(app(Y!47, U!45), X9!49))))) | (~ssList(Z!48)) | (memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49)))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[74, 73])).
% 19.05/19.24 tff(76,plain,
% 19.05/19.24 (memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49))),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[75, 72, 71])).
% 19.05/19.24 tff(77,plain,
% 19.05/19.24 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | ((~ssList(Y!47)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | (~ssList(Y!47)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49)))))),
% 19.05/19.24 inference(rewrite,[status(thm)],[])).
% 19.05/19.24 tff(78,plain,
% 19.05/19.24 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | ((~ssList(Y!47)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49)))))),
% 19.05/19.24 inference(quant_inst,[status(thm)],[])).
% 19.05/19.24 tff(79,plain,
% 19.05/19.24 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (memberP(app(V, W), X9!49) <=> (memberP(W, X9!49) | memberP(V, X9!49)))))) | (~ssList(Y!47)) | ![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49))))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[78, 77])).
% 19.05/19.24 tff(80,plain,
% 19.05/19.24 (![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49))))),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[79, 27, 67])).
% 19.05/19.24 tff(81,plain,
% 19.05/19.24 (((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49))))) | ((~ssList(U!45)) | (memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49))))) | (~ssList(U!45)) | (memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49))))),
% 19.05/19.24 inference(rewrite,[status(thm)],[])).
% 19.05/19.24 tff(82,plain,
% 19.05/19.24 ((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49))))) | ((~ssList(U!45)) | (memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49))))),
% 19.05/19.24 inference(quant_inst,[status(thm)],[])).
% 19.05/19.24 tff(83,plain,
% 19.05/19.24 ((~![W: $i] : ((~ssList(W)) | (memberP(app(Y!47, W), X9!49) <=> (memberP(W, X9!49) | memberP(Y!47, X9!49))))) | (~ssList(U!45)) | (memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49)))),
% 19.05/19.24 inference(modus_ponens,[status(thm)],[82, 81])).
% 19.05/19.24 tff(84,plain,
% 19.05/19.24 (memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49))),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[83, 45, 80])).
% 19.05/19.24 tff(85,plain,
% 19.05/19.24 (memberP(U!45, X9!49)),
% 19.05/19.24 inference(or_elim,[status(thm)],[24])).
% 19.05/19.24 tff(86,plain,
% 19.05/19.24 ((memberP(U!45, X9!49) | memberP(Y!47, X9!49)) | (~memberP(U!45, X9!49))),
% 19.05/19.24 inference(tautology,[status(thm)],[])).
% 19.05/19.24 tff(87,plain,
% 19.05/19.24 (memberP(U!45, X9!49) | memberP(Y!47, X9!49)),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[86, 85])).
% 19.05/19.24 tff(88,plain,
% 19.05/19.24 ((~(memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49)))) | memberP(app(Y!47, U!45), X9!49) | (~(memberP(U!45, X9!49) | memberP(Y!47, X9!49)))),
% 19.05/19.24 inference(tautology,[status(thm)],[])).
% 19.05/19.24 tff(89,plain,
% 19.05/19.24 ((~(memberP(app(Y!47, U!45), X9!49) <=> (memberP(U!45, X9!49) | memberP(Y!47, X9!49)))) | memberP(app(Y!47, U!45), X9!49)),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[88, 87])).
% 19.05/19.24 tff(90,plain,
% 19.05/19.24 (memberP(app(Y!47, U!45), X9!49)),
% 19.05/19.24 inference(unit_resolution,[status(thm)],[89, 84])).
% 19.05/19.24 tff(91,plain,
% 19.05/19.24 ((memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49)) | (~memberP(app(Y!47, U!45), X9!49))),
% 19.05/19.24 inference(tautology,[status(thm)],[])).
% 19.05/19.24 tff(92,plain,
% 19.05/19.24 (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49)),
% 19.12/19.29 inference(unit_resolution,[status(thm)],[91, 90])).
% 19.12/19.29 tff(93,plain,
% 19.12/19.29 ((~(memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49)))) | memberP(app(app(Y!47, U!45), Z!48), X9!49) | (~(memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49)))),
% 19.12/19.29 inference(tautology,[status(thm)],[])).
% 19.12/19.29 tff(94,plain,
% 19.12/19.29 ((~(memberP(app(app(Y!47, U!45), Z!48), X9!49) <=> (memberP(Z!48, X9!49) | memberP(app(Y!47, U!45), X9!49)))) | memberP(app(app(Y!47, U!45), Z!48), X9!49)),
% 19.12/19.29 inference(unit_resolution,[status(thm)],[93, 92])).
% 19.12/19.29 tff(95,plain,
% 19.12/19.29 (memberP(app(app(Y!47, U!45), Z!48), X9!49)),
% 19.12/19.29 inference(unit_resolution,[status(thm)],[94, 76])).
% 19.12/19.29 tff(96,plain,
% 19.12/19.29 ($false),
% 19.12/19.29 inference(unit_resolution,[status(thm)],[95, 26])).
% 19.12/19.29 % SZS output end Proof
% 19.12/19.30 % E exiting
%------------------------------------------------------------------------------