%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC339+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:30:56 AM UTC 2025
% Result : Theorem 15.58s 15.81s
% Output : Proof 15.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC339+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:03:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 15.58/15.81 % SZS status Theorem
% 15.58/15.81 % SZS output start Proof
% 15.58/15.81 tff(tptp_fun_V_46_type, type, (
% 15.58/15.81 tptp_fun_V_46: $i)).
% 15.58/15.81 tff(app_type, type, (
% 15.58/15.81 app: ( $i * $i ) > $i)).
% 15.58/15.81 tff(tptp_fun_U_45_type, type, (
% 15.58/15.81 tptp_fun_U_45: $i)).
% 15.58/15.81 tff(tptp_fun_Y_47_type, type, (
% 15.58/15.81 tptp_fun_Y_47: $i)).
% 15.58/15.81 tff(ssList_type, type, (
% 15.58/15.81 ssList: $i > $o)).
% 15.58/15.81 tff(segmentP_type, type, (
% 15.58/15.81 segmentP: ( $i * $i ) > $o)).
% 15.58/15.81 tff(tptp_fun_X_8_type, type, (
% 15.58/15.81 tptp_fun_X_8: ( $i * $i ) > $i)).
% 15.58/15.81 tff(tptp_fun_W_7_type, type, (
% 15.58/15.81 tptp_fun_W_7: ( $i * $i ) > $i)).
% 15.58/15.81 tff(totalorderedP_type, type, (
% 15.58/15.81 totalorderedP: $i > $o)).
% 15.58/15.81 tff(leq_type, type, (
% 15.58/15.81 leq: ( $i * $i ) > $o)).
% 15.58/15.81 tff(cons_type, type, (
% 15.58/15.81 cons: ( $i * $i ) > $i)).
% 15.58/15.81 tff(nil_type, type, (
% 15.58/15.81 nil: $i)).
% 15.58/15.81 tff(ssItem_type, type, (
% 15.58/15.81 ssItem: $i > $o)).
% 15.58/15.81 tff(tptp_fun_Z_48_type, type, (
% 15.58/15.81 tptp_fun_Z_48: $i)).
% 15.58/15.81 tff(1,plain,
% 15.58/15.81 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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)))))) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))),
% 15.58/15.81 inference(rewrite,[status(thm)],[])).
% 15.58/15.81 tff(2,plain,
% 15.58/15.81 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))),
% 15.58/15.81 inference(rewrite,[status(thm)],[])).
% 15.58/15.81 tff(3,plain,
% 15.58/15.81 ((ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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)))))))),
% 15.58/15.81 inference(rewrite,[status(thm)],[])).
% 15.58/15.81 tff(4,plain,
% 15.58/15.81 ((totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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))))))) <=> (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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)))))))),
% 15.58/15.81 inference(rewrite,[status(thm)],[])).
% 15.58/15.81 tff(5,plain,
% 15.58/15.81 ((ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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))))))))),
% 15.58/15.81 inference(monotonicity,[status(thm)],[4])).
% 15.58/15.81 tff(6,plain,
% 15.58/15.81 ((ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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)))))))),
% 15.58/15.81 inference(transitivity,[status(thm)],[5, 3])).
% 15.58/15.81 tff(7,plain,
% 15.58/15.81 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))),
% 15.58/15.81 inference(monotonicity,[status(thm)],[6])).
% 15.58/15.81 tff(8,plain,
% 15.58/15.81 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45)))) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))),
% 15.58/15.81 inference(transitivity,[status(thm)],[7, 2])).
% 15.58/15.81 tff(9,plain,
% 15.58/15.81 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45)))))),
% 15.58/15.81 inference(monotonicity,[status(thm)],[8])).
% 15.58/15.81 tff(10,plain,
% 15.58/15.81 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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)))))) & (~(segmentP(V!46, U!45) & totalorderedP(U!45))))),
% 15.58/15.81 inference(transitivity,[status(thm)],[9, 1])).
% 15.58/15.81 tff(11,plain,
% 15.58/15.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U)))))),
% 15.58/15.81 inference(rewrite,[status(thm)],[])).
% 15.58/15.81 tff(12,plain,
% 15.58/15.81 ((~![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))))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & totalorderedP(U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U)))))),
% 15.58/15.81 inference(rewrite,[status(thm)],[])).
% 15.58/15.81 tff(13,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))))))))) | ((~(nil = X)) & (nil = W))) | (segmentP(V, U) & totalorderedP(U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 15.58/15.81 tff(14,plain,
% 15.58/15.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U))))),
% 15.58/15.81 inference(modus_ponens,[status(thm)],[13, 12])).
% 15.58/15.81 tff(15,plain,
% 15.58/15.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U))))),
% 15.58/15.81 inference(modus_ponens,[status(thm)],[14, 11])).
% 15.58/15.81 tff(16,plain,
% 15.58/15.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U))))),
% 15.58/15.81 inference(modus_ponens,[status(thm)],[15, 11])).
% 15.58/15.81 tff(17,plain,
% 15.58/15.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~totalorderedP(U)) | (~(app(app(Y, U), Z) = V)) | (~ssList(Z)) | ?[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)) | (segmentP(V, U) & totalorderedP(U))))),
% 15.58/15.81 inference(modus_ponens,[status(thm)],[16, 11])).
% 15.58/15.81 tff(18,plain,
% 15.58/15.81 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & totalorderedP(U!45) & (app(app(Y!47, U!45), Z!48) = V!46) & ssList(Z!48) & ![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)))))) & (~(segmentP(V!46, U!45) & totalorderedP(U!45)))),
% 15.58/15.81 inference(modus_ponens,[status(thm)],[17, 10])).
% 15.58/15.81 tff(19,plain,
% 15.58/15.81 (ssList(V!46)),
% 15.58/15.81 inference(and_elim,[status(thm)],[18])).
% 15.58/15.81 tff(20,plain,
% 15.58/15.81 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 15.58/15.82 inference(bind,[status(th)],[])).
% 15.58/15.82 tff(21,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 15.58/15.82 inference(quant_intro,[status(thm)],[20])).
% 15.58/15.82 tff(22,plain,
% 15.58/15.82 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 15.58/15.82 inference(bind,[status(th)],[])).
% 15.58/15.82 tff(23,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 15.58/15.82 inference(quant_intro,[status(thm)],[22])).
% 15.58/15.82 tff(24,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 15.58/15.82 inference(transitivity,[status(thm)],[23, 21])).
% 15.58/15.82 tff(25,plain,
% 15.58/15.82 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 15.58/15.82 inference(bind,[status(th)],[])).
% 15.58/15.82 tff(26,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 15.58/15.82 inference(quant_intro,[status(thm)],[25])).
% 15.58/15.82 tff(27,plain,
% 15.58/15.82 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))))),
% 15.58/15.82 inference(bind,[status(th)],[])).
% 15.58/15.82 tff(28,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 15.58/15.82 inference(quant_intro,[status(thm)],[27])).
% 15.58/15.82 tff(29,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 15.58/15.82 inference(rewrite,[status(thm)],[])).
% 15.58/15.82 tff(30,plain,
% 15.58/15.82 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))) <=> (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), rewrite((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), (![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))))),
% 15.58/15.82 inference(bind,[status(th)],[])).
% 15.58/15.82 tff(31,plain,
% 15.58/15.82 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 15.58/15.82 inference(quant_intro,[status(thm)],[30])).
% 15.58/15.82 tff(32,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax7')).
% 15.58/15.82 tff(33,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[32, 31])).
% 15.58/15.82 tff(34,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[33, 29])).
% 15.58/15.82 tff(35,plain,(
% 15.58/15.82 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 15.58/15.82 inference(skolemize,[status(sab)],[34])).
% 15.58/15.82 tff(36,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[35, 28])).
% 15.58/15.82 tff(37,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[36, 26])).
% 15.58/15.82 tff(38,plain,
% 15.58/15.82 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[37, 24])).
% 15.58/15.82 tff(39,plain,
% 15.58/15.82 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 15.58/15.82 inference(rewrite,[status(thm)],[])).
% 15.58/15.82 tff(40,plain,
% 15.58/15.82 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46))))))))))),
% 15.58/15.82 inference(quant_inst,[status(thm)],[])).
% 15.58/15.82 tff(41,plain,
% 15.58/15.82 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[40, 39])).
% 15.58/15.82 tff(42,plain,
% 15.58/15.82 (![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))),
% 15.58/15.82 inference(unit_resolution,[status(thm)],[41, 38, 19])).
% 15.58/15.82 tff(43,plain,
% 15.58/15.82 (ssList(U!45)),
% 15.58/15.82 inference(and_elim,[status(thm)],[18])).
% 15.58/15.82 tff(44,plain,
% 15.58/15.82 (((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 15.58/15.82 inference(rewrite,[status(thm)],[])).
% 15.58/15.82 tff(45,plain,
% 15.58/15.82 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | ((~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))))),
% 15.58/15.82 inference(quant_inst,[status(thm)],[])).
% 15.58/15.82 tff(46,plain,
% 15.58/15.82 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(V!46, V)) | (~((~ssList(tptp_fun_W_7(V, V!46))) | (~ssList(tptp_fun_X_8(V, V!46))) | (~(app(app(tptp_fun_W_7(V, V!46), V), tptp_fun_X_8(V, V!46)) = V!46)))))) | (~(segmentP(V!46, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = V!46)))))))))) | (~ssList(U!45)) | (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[45, 44])).
% 15.58/15.82 tff(47,plain,
% 15.58/15.82 (~((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))))),
% 15.58/15.82 inference(unit_resolution,[status(thm)],[46, 43, 42])).
% 15.58/15.82 tff(48,plain,
% 15.58/15.82 (((~((~segmentP(V!46, U!45)) | (~((~ssList(tptp_fun_W_7(U!45, V!46))) | (~ssList(tptp_fun_X_8(U!45, V!46))) | (~(app(app(tptp_fun_W_7(U!45, V!46), U!45), tptp_fun_X_8(U!45, V!46)) = V!46)))))) | (~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))))) | (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))),
% 15.58/15.82 inference(tautology,[status(thm)],[])).
% 15.58/15.82 tff(49,plain,
% 15.58/15.82 (segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 15.58/15.82 inference(unit_resolution,[status(thm)],[48, 47])).
% 15.58/15.82 tff(50,plain,
% 15.58/15.82 (totalorderedP(U!45)),
% 15.58/15.82 inference(and_elim,[status(thm)],[18])).
% 15.58/15.82 tff(51,plain,
% 15.58/15.82 ((~(~((~totalorderedP(U!45)) | (~segmentP(V!46, U!45))))) <=> ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)))),
% 15.58/15.82 inference(rewrite,[status(thm)],[])).
% 15.58/15.82 tff(52,plain,
% 15.58/15.82 ((segmentP(V!46, U!45) & totalorderedP(U!45)) <=> (~((~totalorderedP(U!45)) | (~segmentP(V!46, U!45))))),
% 15.58/15.82 inference(rewrite,[status(thm)],[])).
% 15.58/15.82 tff(53,plain,
% 15.58/15.82 ((~(segmentP(V!46, U!45) & totalorderedP(U!45))) <=> (~(~((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)))))),
% 15.58/15.82 inference(monotonicity,[status(thm)],[52])).
% 15.58/15.82 tff(54,plain,
% 15.58/15.82 ((~(segmentP(V!46, U!45) & totalorderedP(U!45))) <=> ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)))),
% 15.58/15.82 inference(transitivity,[status(thm)],[53, 51])).
% 15.58/15.82 tff(55,plain,
% 15.58/15.82 (~(segmentP(V!46, U!45) & totalorderedP(U!45))),
% 15.58/15.82 inference(and_elim,[status(thm)],[18])).
% 15.58/15.82 tff(56,plain,
% 15.58/15.82 ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45))),
% 15.58/15.82 inference(modus_ponens,[status(thm)],[55, 54])).
% 15.58/15.82 tff(57,plain,
% 15.58/15.82 (~segmentP(V!46, U!45)),
% 15.58/15.82 inference(unit_resolution,[status(thm)],[56, 50])).
% 15.58/15.82 tff(58,plain,
% 15.58/15.82 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 15.58/15.82 inference(tautology,[status(thm)],[])).
% 15.58/15.82 tff(59,plain,
% 15.58/15.82 ((~(segmentP(V!46, U!45) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46)))))) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 15.58/15.82 inference(unit_resolution,[status(thm)],[58, 57])).
% 15.58/15.82 tff(60,plain,
% 15.58/15.82 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))),
% 15.58/15.82 inference(unit_resolution,[status(thm)],[59, 49])).
% 15.58/15.82 tff(61,plain,
% 15.58/15.82 (ssList(Y!47)),
% 15.58/15.82 inference(and_elim,[status(thm)],[18])).
% 15.58/15.82 tff(62,plain,
% 15.58/15.82 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(Y!47)) | ![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(Y!47)) | ![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46))))),
% 15.58/15.82 inference(rewrite,[status(thm)],[])).
% 15.68/15.87 tff(63,plain,
% 15.68/15.87 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | ((~ssList(Y!47)) | ![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46))))),
% 15.68/15.87 inference(quant_inst,[status(thm)],[])).
% 15.68/15.87 tff(64,plain,
% 15.68/15.87 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, U!45), X) = V!46))))) | (~ssList(Y!47)) | ![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46)))),
% 15.68/15.87 inference(modus_ponens,[status(thm)],[63, 62])).
% 15.68/15.87 tff(65,plain,
% 15.68/15.87 (![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46)))),
% 15.68/15.87 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 15.68/15.87 tff(66,plain,
% 15.68/15.87 (ssList(Z!48)),
% 15.68/15.87 inference(and_elim,[status(thm)],[18])).
% 15.68/15.87 tff(67,plain,
% 15.68/15.87 (app(app(Y!47, U!45), Z!48) = V!46),
% 15.68/15.87 inference(and_elim,[status(thm)],[18])).
% 15.68/15.87 tff(68,plain,
% 15.68/15.87 (((~![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46)))) | ((~ssList(Z!48)) | (~(app(app(Y!47, U!45), Z!48) = V!46)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46)))) | (~ssList(Z!48)) | (~(app(app(Y!47, U!45), Z!48) = V!46)))),
% 15.68/15.87 inference(rewrite,[status(thm)],[])).
% 15.68/15.87 tff(69,plain,
% 15.68/15.87 ((~![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46)))) | ((~ssList(Z!48)) | (~(app(app(Y!47, U!45), Z!48) = V!46)))),
% 15.68/15.87 inference(quant_inst,[status(thm)],[])).
% 15.68/15.87 tff(70,plain,
% 15.68/15.87 ((~![X: $i] : ((~ssList(X)) | (~(app(app(Y!47, U!45), X) = V!46)))) | (~ssList(Z!48)) | (~(app(app(Y!47, U!45), Z!48) = V!46))),
% 15.68/15.87 inference(modus_ponens,[status(thm)],[69, 68])).
% 15.68/15.87 tff(71,plain,
% 15.68/15.87 ($false),
% 15.68/15.87 inference(unit_resolution,[status(thm)],[70, 67, 66, 65])).
% 15.68/15.87 % SZS output end Proof
% 15.68/15.88 % E exiting
%------------------------------------------------------------------------------