%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC213+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:32 AM UTC 2025
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC213+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 08:38:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(tptp_fun_U_45_type, type, (
% 0.19/0.49 tptp_fun_U_45: $i)).
% 0.19/0.49 tff(nil_type, type, (
% 0.19/0.49 nil: $i)).
% 0.19/0.49 tff(neq_type, type, (
% 0.19/0.49 neq: ( $i * $i ) > $o)).
% 0.19/0.49 tff(ssList_type, type, (
% 0.19/0.49 ssList: $i > $o)).
% 0.19/0.49 tff(tptp_fun_V_46_type, type, (
% 0.19/0.49 tptp_fun_V_46: $i)).
% 0.19/0.49 tff(app_type, type, (
% 0.19/0.49 app: ( $i * $i ) > $i)).
% 0.19/0.49 tff(cons_type, type, (
% 0.19/0.49 cons: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_Z_48_type, type, (
% 0.19/0.49 tptp_fun_Z_48: $i)).
% 0.19/0.49 tff(ssItem_type, type, (
% 0.19/0.49 ssItem: $i > $o)).
% 0.19/0.49 tff(tptp_fun_Y_47_type, type, (
% 0.19/0.49 tptp_fun_Y_47: $i)).
% 0.19/0.49 tff(equalelemsP_type, type, (
% 0.19/0.49 equalelemsP: $i > $o)).
% 0.19/0.49 tff(segmentP_type, type, (
% 0.19/0.49 segmentP: ( $i * $i ) > $o)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(2,plain,
% 0.19/0.49 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45)))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(3,plain,
% 0.19/0.49 ((ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) <=> (ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(4,plain,
% 0.19/0.49 (((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45)))))) <=> ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 ((ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) <=> (ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45)))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[4])).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 ((ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) <=> (ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45)))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.19/0.50 inference(transitivity,[status(thm)],[7, 2])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[8])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (ssList(Y!47) & ((app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.19/0.50 inference(transitivity,[status(thm)],[9, 1])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W))))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : ((ssList(X5) & (app(cons(X4, nil), X5) = Z)) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W)))))))) | neq(U, nil)) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(13,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((((~(app(app(Y, W), Z) = X)) | (~equalelemsP(W))) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : ((ssList(X2) & (app(X2, cons(X1, nil)) = Y)) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = W))))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : ((ssList(X5) & (app(cons(X4, nil), X5) = Z)) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = W)))))))) | neq(U, nil)) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(app(Y, U), Z) = V)) | (~equalelemsP(U)) | (~ssList(Z)) | ?[X1: $i] : (ssItem(X1) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(X1, nil)) = Y) & ?[X3: $i] : (ssList(X3) & (app(cons(X1, nil), X3) = U)))) | ?[X4: $i] : (ssItem(X4) & ?[X5: $i] : (ssList(X5) & (app(cons(X4, nil), X5) = Z) & ?[X6: $i] : (ssList(X6) & (app(X6, cons(X4, nil)) = U)))))) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ssList(Y!47) & (app(app(Y!47, U!45), Z!48) = V!46) & equalelemsP(U!45) & ssList(Z!48) & ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(app(X2, cons(X1, nil)) = Y!47)) | ![X3: $i] : (~(ssList(X3) & (app(cons(X1, nil), X3) = U!45))))) & ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | (~(app(cons(X4, nil), X5) = Z!48)) | ![X6: $i] : (~(ssList(X6) & (app(X6, cons(X4, nil)) = U!45))))) & (~neq(U!45, nil)) & neq(V!46, nil)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (ssList(U!45)),
% 0.19/0.50 inference(and_elim,[status(thm)],[18])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.50 tff(28,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.50 tff(31,plain,(
% 0.19/0.50 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[30])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 (ssList(nil) <=> ssList(nil)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(38,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (ssList(nil)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[42, 39, 36])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (~neq(U!45, nil)),
% 0.19/0.50 inference(and_elim,[status(thm)],[18])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(46,plain,
% 0.19/0.50 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (U!45 = nil),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 (nil = U!45),
% 0.19/0.50 inference(symmetry,[status(thm)],[47])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (ssList(V!46)),
% 0.19/0.50 inference(and_elim,[status(thm)],[18])).
% 0.19/0.50 tff(50,plain,
% 0.19/0.50 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(53,plain,
% 0.19/0.50 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.50 tff(55,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.51 tff(58,plain,(
% 0.19/0.51 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[57])).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(62,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 0.19/0.51 tff(64,plain,
% 0.19/0.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(66,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[66, 32, 49])).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[70, 39, 67])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (neq(V!46, nil)),
% 0.19/0.51 inference(and_elim,[status(thm)],[18])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.51 tff(75,plain,
% 0.19/0.51 (~(V!46 = nil)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.51 tff(78,plain,
% 0.19/0.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.51 tff(86,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.51 tff(88,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.51 tff(89,plain,(
% 0.19/0.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[88])).
% 0.19/0.51 tff(90,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.51 tff(91,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.19/0.51 tff(92,plain,
% 0.19/0.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(93,plain,
% 0.19/0.51 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(94,plain,
% 0.19/0.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.51 tff(95,plain,
% 0.19/0.51 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.51 tff(96,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(97,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.51 tff(98,plain,
% 0.19/0.51 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[97, 91, 49])).
% 0.19/0.51 tff(99,plain,
% 0.19/0.51 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(100,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.51 tff(101,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(102,plain,
% 0.19/0.51 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(103,plain,
% 0.19/0.51 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.51 tff(104,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.19/0.51 tff(105,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.51 tff(106,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.51 tff(107,plain,(
% 0.19/0.51 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(skolemize,[status(sab)],[106])).
% 0.19/0.51 tff(108,plain,
% 0.19/0.51 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.51 tff(109,plain,
% 0.19/0.51 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(110,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(111,plain,
% 0.19/0.51 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.51 tff(112,plain,
% 0.19/0.51 (segmentP(V!46, nil)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[111, 108, 49])).
% 0.19/0.51 tff(113,plain,
% 0.19/0.51 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(114,plain,
% 0.19/0.51 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(115,plain,
% 0.19/0.51 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.51 tff(116,plain,
% 0.19/0.51 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[115, 113])).
% 0.19/0.51 tff(117,plain,
% 0.19/0.51 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(118,plain,
% 0.19/0.51 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.51 tff(119,plain,
% 0.19/0.51 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[118, 39, 112, 98])).
% 0.19/0.51 tff(120,plain,
% 0.19/0.51 (~segmentP(nil, V!46)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[119, 75])).
% 0.19/0.51 tff(121,plain,
% 0.19/0.51 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(122,plain,
% 0.19/0.51 (~(nil = V!46)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[121, 120, 63])).
% 0.19/0.51 tff(123,plain,
% 0.19/0.51 ((~(~((nil = V!46) | (~(nil = U!45))))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(124,plain,
% 0.19/0.51 (((~(nil = V!46)) & (nil = U!45)) <=> (~((nil = V!46) | (~(nil = U!45))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 ((~((~(nil = V!46)) & (nil = U!45))) <=> (~(~((nil = V!46) | (~(nil = U!45)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 ((~((~(nil = V!46)) & (nil = U!45))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[125, 123])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (~((~(nil = V!46)) & (nil = U!45))),
% 0.19/0.51 inference(and_elim,[status(thm)],[18])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 ((nil = V!46) | (~(nil = U!45))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 (~(nil = U!45)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[128, 122])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[129, 48])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------