%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC189+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 05:30:27 AM UTC 2025
% Result : Theorem 21.95s 22.16s
% Output : Proof 22.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC189+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:32:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 21.95/22.16 % SZS status Theorem
% 21.95/22.16 % SZS output start Proof
% 21.95/22.16 tff(tptp_fun_U_45_type, type, (
% 21.95/22.16 tptp_fun_U_45: $i)).
% 21.95/22.16 tff(app_type, type, (
% 21.95/22.16 app: ( $i * $i ) > $i)).
% 21.95/22.16 tff(cons_type, type, (
% 21.95/22.16 cons: ( $i * $i ) > $i)).
% 21.95/22.16 tff(nil_type, type, (
% 21.95/22.16 nil: $i)).
% 21.95/22.16 tff(tptp_fun_X4_48_type, type, (
% 21.95/22.16 tptp_fun_X4_48: $i)).
% 21.95/22.16 tff(tptp_fun_X3_47_type, type, (
% 21.95/22.16 tptp_fun_X3_47: $i)).
% 21.95/22.16 tff(tptp_fun_X5_49_type, type, (
% 21.95/22.16 tptp_fun_X5_49: $i)).
% 21.95/22.16 tff(ssList_type, type, (
% 21.95/22.16 ssList: $i > $o)).
% 21.95/22.16 tff(ssItem_type, type, (
% 21.95/22.16 ssItem: $i > $o)).
% 21.95/22.16 tff(tptp_fun_X6_50_type, type, (
% 21.95/22.16 tptp_fun_X6_50: $i)).
% 21.95/22.16 tff(tptp_fun_V_46_type, type, (
% 21.95/22.16 tptp_fun_V_46: $i)).
% 21.95/22.16 tff(1,plain,
% 21.95/22.16 ((ssList(U!45) & (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(2,plain,
% 21.95/22.16 ((ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & (ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))) <=> (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(3,plain,
% 21.95/22.16 ((ssItem(X3!47) & (ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))) <=> (ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(4,plain,
% 21.95/22.16 ((ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))) <=> (ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(5,plain,
% 21.95/22.16 ((~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))) <=> (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(6,plain,
% 21.95/22.16 ((ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))) <=> (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(monotonicity,[status(thm)],[5])).
% 21.95/22.16 tff(7,plain,
% 21.95/22.16 ((ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))) <=> (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))),
% 21.95/22.16 inference(monotonicity,[status(thm)],[6])).
% 21.95/22.16 tff(8,plain,
% 21.95/22.16 ((ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))) <=> (ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(transitivity,[status(thm)],[7, 4])).
% 21.95/22.16 tff(9,plain,
% 21.95/22.16 ((ssItem(X3!47) & (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))) <=> (ssItem(X3!47) & (ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))),
% 21.95/22.16 inference(monotonicity,[status(thm)],[8])).
% 21.95/22.16 tff(10,plain,
% 21.95/22.16 ((ssItem(X3!47) & (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))) <=> (ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(transitivity,[status(thm)],[9, 3])).
% 21.95/22.16 tff(11,plain,
% 21.95/22.16 ((ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & (ssItem(X3!47) & (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))))) <=> (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & (ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))),
% 21.95/22.16 inference(monotonicity,[status(thm)],[10])).
% 21.95/22.16 tff(12,plain,
% 21.95/22.16 ((ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & (ssItem(X3!47) & (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))))) <=> (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(transitivity,[status(thm)],[11, 2])).
% 21.95/22.16 tff(13,plain,
% 21.95/22.16 ((ssList(U!45) & (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & (ssItem(X3!47) & (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))))) <=> (ssList(U!45) & (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))),
% 21.95/22.16 inference(monotonicity,[status(thm)],[12])).
% 21.95/22.16 tff(14,plain,
% 21.95/22.16 ((ssList(U!45) & (ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssList(U!45) & (ssItem(X3!47) & (ssItem(X4!48) & (ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))))))) <=> (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))))),
% 21.95/22.16 inference(transitivity,[status(thm)],[13, 1])).
% 21.95/22.16 tff(15,plain,
% 21.95/22.16 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)))))))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(16,plain,
% 21.95/22.16 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : ((ssList(X2) & (~(Y = Z))) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W)))))) | ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssItem(X4) => ![X5: $i] : (ssList(X5) => ![X6: $i] : (ssList(X6) => ((~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (X3 = X4)))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)))))))))),
% 21.95/22.16 inference(rewrite,[status(thm)],[])).
% 21.95/22.16 tff(17,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : ((ssList(X2) & (~(Y = Z))) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = W)))))) | ![X3: $i] : (ssItem(X3) => ![X4: $i] : (ssItem(X4) => ![X5: $i] : (ssList(X5) => ![X6: $i] : (ssList(X6) => ((~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U)) | (X3 = X4)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 21.95/22.16 tff(18,plain,
% 21.95/22.16 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U))))))))),
% 21.95/22.16 inference(modus_ponens,[status(thm)],[17, 16])).
% 21.95/22.16 tff(19,plain,
% 21.95/22.16 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U))))))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[18, 15])).
% 21.95/22.17 tff(20,plain,
% 21.95/22.17 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U))))))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[19, 15])).
% 21.95/22.17 tff(21,plain,
% 21.95/22.17 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & ?[X2: $i] : (ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U))))) | (~ssList(U)) | ![X3: $i] : ((~ssItem(X3)) | ![X4: $i] : ((~ssItem(X4)) | ![X5: $i] : ((~ssList(X5)) | ![X6: $i] : ((X3 = X4) | (~ssList(X6)) | (~(app(app(app(X5, cons(X3, nil)), cons(X4, nil)), X6) = U))))))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[20, 15])).
% 21.95/22.17 tff(22,plain,
% 21.95/22.17 (ssList(U!45) & ssList(V!46) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) & ssItem(X3!47) & ssItem(X4!48) & ssList(X5!49) & (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[21, 14])).
% 21.95/22.17 tff(23,plain,
% 21.95/22.17 (ssItem(X3!47)),
% 21.95/22.17 inference(and_elim,[status(thm)],[22])).
% 21.95/22.17 tff(24,plain,
% 21.95/22.17 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))))),
% 21.95/22.17 inference(bind,[status(th)],[])).
% 21.95/22.17 tff(25,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(quant_intro,[status(thm)],[24])).
% 21.95/22.17 tff(26,plain,
% 21.95/22.17 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))))),
% 21.95/22.17 inference(bind,[status(th)],[])).
% 21.95/22.17 tff(27,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(quant_intro,[status(thm)],[26])).
% 21.95/22.17 tff(28,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(transitivity,[status(thm)],[27, 25])).
% 21.95/22.17 tff(29,plain,
% 21.95/22.17 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))))),
% 21.95/22.17 inference(bind,[status(th)],[])).
% 21.95/22.17 tff(30,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(quant_intro,[status(thm)],[29])).
% 21.95/22.17 tff(31,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : (~(ssList(X2) & (~(Y = Z)) & (app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(and_elim,[status(thm)],[22])).
% 21.95/22.17 tff(32,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[31, 30])).
% 21.95/22.17 tff(33,plain,
% 21.95/22.17 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[32, 28])).
% 21.95/22.17 tff(34,plain,
% 21.95/22.17 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(rewrite,[status(thm)],[])).
% 21.95/22.17 tff(35,plain,
% 21.95/22.17 (((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!47 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))) <=> ((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(rewrite,[status(thm)],[])).
% 21.95/22.17 tff(36,plain,
% 21.95/22.17 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!47 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))))),
% 21.95/22.17 inference(monotonicity,[status(thm)],[35])).
% 21.95/22.17 tff(37,plain,
% 21.95/22.17 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!47 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(transitivity,[status(thm)],[36, 34])).
% 21.95/22.17 tff(38,plain,
% 21.95/22.17 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | ((~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((X3!47 = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45))))))),
% 21.95/22.17 inference(quant_inst,[status(thm)],[])).
% 21.95/22.17 tff(39,plain,
% 21.95/22.17 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((Y = Z) | (~ssList(X2)) | (~(app(app(app(X1, cons(Y, nil)), cons(Z, nil)), X2) = U!45))))))) | (~ssItem(X3!47)) | ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[38, 37])).
% 21.95/22.17 tff(40,plain,
% 21.95/22.17 (![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))),
% 21.95/22.17 inference(unit_resolution,[status(thm)],[39, 33, 23])).
% 21.95/22.17 tff(41,plain,
% 21.95/22.17 (ssItem(X4!48)),
% 21.95/22.17 inference(and_elim,[status(thm)],[22])).
% 21.95/22.17 tff(42,plain,
% 21.95/22.17 (((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))) | ((~ssItem(X4!48)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))))) <=> ((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))) | (~ssItem(X4!48)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))))),
% 21.95/22.17 inference(rewrite,[status(thm)],[])).
% 21.95/22.17 tff(43,plain,
% 21.95/22.17 ((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))) | ((~ssItem(X4!48)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))))),
% 21.95/22.17 inference(quant_inst,[status(thm)],[])).
% 21.95/22.17 tff(44,plain,
% 21.95/22.17 ((~![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = Z) | (~(app(app(app(X1, cons(X3!47, nil)), cons(Z, nil)), X2) = U!45)))))) | (~ssItem(X4!48)) | ![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[43, 42])).
% 21.95/22.17 tff(45,plain,
% 21.95/22.17 (![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))),
% 21.95/22.17 inference(unit_resolution,[status(thm)],[44, 41, 40])).
% 21.95/22.17 tff(46,plain,
% 21.95/22.17 (ssList(X5!49)),
% 21.95/22.17 inference(and_elim,[status(thm)],[22])).
% 21.95/22.17 tff(47,plain,
% 21.95/22.17 (((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))) | ((~ssList(X5!49)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))) <=> ((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))) | (~ssList(X5!49)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))),
% 21.95/22.17 inference(rewrite,[status(thm)],[])).
% 21.95/22.17 tff(48,plain,
% 21.95/22.17 ((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))) | ((~ssList(X5!49)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))),
% 21.95/22.17 inference(quant_inst,[status(thm)],[])).
% 21.95/22.17 tff(49,plain,
% 21.95/22.17 ((~![X1: $i] : ((~ssList(X1)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X1, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45))))) | (~ssList(X5!49)) | ![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[48, 47])).
% 21.95/22.17 tff(50,plain,
% 21.95/22.17 (![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))),
% 21.95/22.17 inference(unit_resolution,[status(thm)],[49, 46, 45])).
% 21.95/22.17 tff(51,plain,
% 21.95/22.17 (~((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))),
% 21.95/22.17 inference(and_elim,[status(thm)],[22])).
% 21.95/22.17 tff(52,plain,
% 21.95/22.17 (app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45),
% 21.95/22.17 inference(or_elim,[status(thm)],[51])).
% 21.95/22.17 tff(53,plain,
% 21.95/22.17 (ssList(X6!50)),
% 21.95/22.17 inference(or_elim,[status(thm)],[51])).
% 21.95/22.17 tff(54,plain,
% 21.95/22.17 (~(X3!47 = X4!48)),
% 21.95/22.17 inference(or_elim,[status(thm)],[51])).
% 21.95/22.17 tff(55,plain,
% 21.95/22.17 (((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | ((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))) <=> ((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | (X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))),
% 21.95/22.17 inference(rewrite,[status(thm)],[])).
% 21.95/22.17 tff(56,plain,
% 21.95/22.17 (((~ssList(X6!50)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))) <=> ((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))),
% 21.95/22.17 inference(rewrite,[status(thm)],[])).
% 21.95/22.17 tff(57,plain,
% 21.95/22.17 (((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | ((~ssList(X6!50)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))) <=> ((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | ((X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))))),
% 21.95/22.17 inference(monotonicity,[status(thm)],[56])).
% 21.95/22.17 tff(58,plain,
% 21.95/22.17 (((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | ((~ssList(X6!50)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))) <=> ((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | (X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))),
% 21.95/22.17 inference(transitivity,[status(thm)],[57, 55])).
% 21.95/22.17 tff(59,plain,
% 21.95/22.17 ((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | ((~ssList(X6!50)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45)))),
% 21.95/22.17 inference(quant_inst,[status(thm)],[])).
% 21.95/22.17 tff(60,plain,
% 21.95/22.17 ((~![X2: $i] : ((~ssList(X2)) | (X3!47 = X4!48) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X2) = U!45)))) | (X3!47 = X4!48) | (~ssList(X6!50)) | (~(app(app(app(X5!49, cons(X3!47, nil)), cons(X4!48, nil)), X6!50) = U!45))),
% 21.95/22.17 inference(modus_ponens,[status(thm)],[59, 58])).
% 21.95/22.17 tff(61,plain,
% 21.95/22.17 ($false),
% 21.95/22.17 inference(unit_resolution,[status(thm)],[60, 54, 53, 52, 50])).
% 22.03/22.23 % SZS output end Proof
% 22.03/22.24 % E exiting
%------------------------------------------------------------------------------